How long before the end of inflation were observable perturbations produced?
Open accessAbstract
We reconsider the issue of the number of e-foldings before the end of inflation at which observable perturbations were generated. We determine a plausible upper limit on that number for the standard cosmology which is around 60, with the expectation that the actual value will be up to 10 below this. We also note a special property of the $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ model which reduces the uncertainties in that case and favors a higher value, giving a fairly definite prediction of 64 e-foldings for that model. We note an extreme (and highly implausible) situation where the number of e-foldings can be even higher, possibly up to 100, and discuss the shortcomings of quantifying inflation by e-foldings rather than by the change in $\mathrm{aH}.$ Finally, we discuss the impact of nonstandard evolution between the end of inflation and the present, showing that again the expected number of e-foldings can be modified, and in some cases significantly increased.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
An Alternative to Compactification
Randall, L., & Sundrum, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.4690 · Cited by 7,217 · see citing works
Cosmological Inflation and Large-Scale Structure
Liddle, A. R., & Lyth, D. H. (2000) · doi:10.1017/cbo9781139175180 · Cited by 2,317 · see citing works
Self-citationTowards the theory of reheating after inflation
Kofman, L. A., Linde, A. D., & Starobinsky, A. A. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.56.3258 · Cited by 1,987 · see citing works
First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Implications For Inflation
Peiris, H. V., Komatsu, E., Verde, L., Spergel, D. N., Bennett, C. L., Halpern, M., Hinshaw, G. F., Jarosik, N., Kogut, A., Limon, M., et al. (2003) · The Astrophysical Journal Supplement Series · doi:10.1086/377228 · Cited by 1,159 · see citing works
Particle production during out-of-equilibrium phase transitions
Traschen, J., & Brandenberger, R. (1990) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.42.2491 · Cited by 949 · see citing works
Cosmology with a primordial scaling field
Ferreira, P. G., & Joyce, M. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.58.023503 · Cited by 895 · see citing works
The cold dark matter density perturbation
Liddle, A. R., & Lyth, D. H. (1993) · Physics Reports · doi:10.1016/0370-1573(93)90114-s · Cited by 718 · see citing works
Self-citationFormalizing the slow-roll approximation in inflation
Liddle, A. R., Parsons, P., & Barrow, J. D. (1994) · Physical Review D · doi:10.1103/physrevd.50.7222 · Cited by 714 · see citing works
Self-citationPeebles, P. J. E., & Vilenkin, A. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.59.063505 · Cited by 628 · see citing works
Gravitational particle creation and inflation
Ford, L. H. (1987) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.35.2955 · Cited by 590 · see citing works
de Carlos, B., Casas, J. A., Quevedo, F., & Roulet, E. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)91538-x · Cited by 568 · see citing works
Cosmological implications of dynamical supersymmetry breaking
Banks, T., Kaplan, D. B., & Nelson, A. E. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.779 · Cited by 545 · see citing works
Chaotic inflation on the brane
Maartens, R., Wands, D., Bassett, B. A., & Heard, I. P. C. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.041301 · Cited by 499 · see citing works
Thermal inflation and the moduli problem
Lyth, D. H., & Stewart, E. D. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.53.1784 · Cited by 497 · see citing works
Squeezed quantum states of relic gravitons and primordial density fluctuations
Грищук, Л. П., & Sidorov, Y. V. (1990) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.42.3413 · Cited by 492 · see citing works
Deflationary Universe scenario
Spokoiny, B. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)90155-b · Cited by 308 · see citing works
Cosmology with a TeV Mass Higgs Field Breaking the Grand-Unified-Theory Gauge Symmetry
Lyth, D. H., & Stewart, E. D. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.201 · Cited by 266 · see citing works
Metric perturbations in two-field inflation
García-Bellido, J., & Wands, D. (1996) · Physical Review D · doi:10.1103/physrevd.53.5437 · Cited by 253 · see citing works
Gravitino production in the inflationary universe and the effects on big-bang nucleosynthesis
Kawasaki, M., & Moroi, T. (1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 248 · see citing works
Relic gravity waves from braneworld inflation
Varun Sahni, A., Sami, M., & Souradeep, T. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.65.023518 · Cited by 217 · see citing works
Electroweak baryogenesis and the expansion rate of the Universe
Joyce, M. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.55.1875 · Cited by 217 · see citing works
Gravitino Production in the Inflationary Universe and the Effects on Big-Bang Nucleosynthesis
Kawasaki, M., & Moroi, T. (1995) · Progress of Theoretical Physics · doi:10.1143/ptp/93.5.879 · Cited by 206 · see citing works
Steep inflation: Ending braneworld inflation by gravitational particle production
Copeland, E. J., Liddle, A. R., & Lidsey, J. E. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.023509 · Cited by 191 · see citing works
Self-citationCosmological perturbations from multi-field inflation in generalized Einstein theories
Starobinsky, A. A., Tsujikawa, S., & Yokoyama, J. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00322-4 · Cited by 164 · see citing works
Linde, A. (2001) · Journal of High Energy Physics · doi:10.1088/1126-6708/2001/11/052 · Cited by 144 · see citing works
Adiabatic and isocurvature perturbations from inflation: Power spectra and consistency relations
Bartolo, N., Matarrese, S., & Riotto, A. W. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.123504 · Cited by 137 · see citing works
Horizon Ratio Bound for Inflationary Fluctuations
Dodelson, S., & Hui, L. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.131301 · Cited by 134 · see citing works
Barger, V. D., Lee, H., & Marfatia, D. (2003) · Physics Letters B · doi:10.1016/s0370-2693(03)00757-3 · Cited by 95 · see citing works
Correlation-consistency cartography of the double-inflation landscape
Tsujikawa, S., Parkinson, D., & Bassett, B. A. (2003) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.67.083516 · Cited by 93 · see citing works
Microwave background constraints on inflationary parameters
Leach, S. M., & Liddle, A. R. (2003) · Monthly Notices of the Royal Astronomical Society · doi:10.1046/j.1365-8711.2003.06445.x · Cited by 39 · see citing works
Self-citationDensity fluctuations in Brans-Dicke inflationPreprint
Starobinsky, A. A., & Yokoyama, J. (1995) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9502002 · Cited by 36 · see citing works
Felder, G., Kofman, L. A., Linde, A. D., & Tkachev, I. I. (2000) · Journal of High Energy Physics · doi:10.1088/1126-6708/2000/08/010 · Cited by 32 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- [7]7. ͓7͔ S. M. Leach and A. R. Liddle, Phys. Rev. D ͑to be published͒, astro-ph/0306305. · arXiv
Cited by
Sorted by citations
FIVE-YEAR<i>WILKINSON MICROWAVE ANISOTROPY PROBE</i>OBSERVATIONS: COSMOLOGICAL INTERPRETATION
Komatsu, E., Dunkley, J., Nolta, M. R., Bennett, C. L., Gold, B., Hinshaw, G., Jarosik, N., Larson, D., Limon, M., Page, L., et al. (2009) · The Astrophysical Journal Supplement Series · doi:10.1088/0067-0049/180/2/330 · Cited by 5,786 · see citing works
Cosmological parameters from SDSS and WMAP
Tegmark, M., Strauss, M. A., Blanton, M. R., Abazajian, K. N., Dodelson, S., Sandvik, H. B., Wang, X., Weinberg, D. H., Zehavi, I., Bahcall, N. A., et al. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.69.103501 · Cited by 3,990 · see citing works
Akrami, Y., Arroja, F. M. A., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., Basak, S., et al. (2019) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201833887 · Cited by 2,435 · see citing works
Ade, P. A. R., Aghanim, N., Arnaud, M., Arroja, F. M. A., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., et al. (2016) · Repository@Nottingham (University of Nottingham) · doi:10.17863/cam.52 · Cited by 1,925 · see citing works
Cosmological constraints from the SDSS luminous red galaxies
Tegmark, M., Eisenstein, D. J., Strauss, M. A., Weinberg, D. H., Blanton, M. R., Frieman, J. A., Fukugita, M., Gunn, J. E., Hamilton, A. J. S., Knapp, G. R., et al. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.74.123507 · Cited by 1,405 · see citing works
Ade, P. A. R., Aghanim, N., Arnaud, M., Arroja, F. M. A., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., et al. (2016) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201525898 · Cited by 1,402 · see citing works
Planck 2013 results. XXII. Constraints on inflation
Ade, P. A. R., Aghanim, N., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., Aumont, J., Baccigalupi, C., Banday, A. J., Barreiro, R. B., et al. (2014) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201321569 · Cited by 1,082 · see citing works
Martin, J., Ringeval, C., & Vennin, V. (2024) · Physics of the Dark Universe · doi:10.1016/j.dark.2014.01.003 · Cited by 396 · see citing works
Seljak, U., Makarov, A., McDonald, P., Anderson, S. F., Bahcall, N. A., Brinkmann, J., Burles, S. M., Cen, R., Doi, M., Gunn, J. E., et al. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.71.103515 · Cited by 1,041 · see citing works
Inflation dynamics and reheating
Bassett, B. A., Tsujikawa, S., & Wands, D. (2006) · Reviews of Modern Physics · doi:10.1103/revmodphys.78.537 · Cited by 1,022 · see citing works
The landscape of QCD axion models
Luzio, L. D., Giannotti, M., Nardi, E., & Visinelli, L. (2020) · Physics Reports · doi:10.1016/j.physrep.2020.06.002 · Cited by 741 · see citing works
Teleparallel gravity: from theory to cosmology
Bahamonde, S., Dialektopoulos, K. F., Escamilla‐Rivera, C., Farrugia, G., Gakis, V., Hendry, M., Hohmann, M., Said, J. L., Mifsud, J., & Valentino, E. D. (2022) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac9cef · Cited by 506 · see citing works
Nonperturbative dynamics of reheating after inflation: A review
Amin, M. A., Hertzberg, M. P., Kaiser, D. I., & Karouby, J. (2014) · International Journal of Modern Physics D · doi:10.1142/s0218271815300037 · Cited by 498 · see citing works
Primordial black hole dark matter from single field inflation
Ballesteros, G., & Marco Taoso, A. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.023501 · Cited by 339 · see citing works
First CMB constraints on the inflationary reheating temperature
Martin, J., & Ringeval, C. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.023511 · Cited by 334 · see citing works
Green, A. M., Hofmann, S., & Schwarz, D. J. (2005) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2005/08/003 · Cited by 307 · see citing works
Gauge-invariant inflaton in the minimal supersymmetric standard model
Allahverdi, R., Enqvist, K., García-Bellido, J., & Mazumdar, A. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.191304 · Cited by 295 · see citing works
Scalaron from R 2 -gravity as a heavy field
Pi, S., Zhang, Y.-L., Huang, Q.-G., & Sasaki, M. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/05/042 · Cited by 289 · see citing works
Reheating Constraints to Inflationary Models
Dai, L., Kamionkowski, M., & Wang, J. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.041302 · Cited by 286 · see citing works
Reheating predictions in single field inflation
Cook, J. L., Dimastrogiovanni, E., Easson, D. A., & Krauss, L. M. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/04/047 · Cited by 271 · see citing works
Micha, R., & Tkachev, I. I. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.043538 · Cited by 263 · see citing works
Calculating the mass fraction of primordial black holes
Young, S., Byrnes, C. T., & Sasaki, M. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/07/045 · Cited by 254 · see citing works
Review of cosmic phase transitions: their significance and experimental signatures
Mazumdar, A., & White, G. (2019) · Reports on Progress in Physics · doi:10.1088/1361-6633/ab1f55 · Cited by 249 · see citing works
The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe
Allahverdi, R., Amin, M. A., Berlin, A., Bernal, N., Byrnes, C. T., Delos, M. S., Erickcek, A. L., Escudero, M., Figueroa, D. G., Katherine Freese, B., et al. (2021) · The Open Journal of Astrophysics · doi:10.21105/astro.2006.16182 · Cited by 268 · see citing works
Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data
Martin, J., & Ringeval, C. (2006) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2006/08/009 · Cited by 241 · see citing works
Self-resonance after inflation: Oscillons, transients, and radiation domination
Lozanov, K. D., & Amin, M. A. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.023533 · Cited by 228 · see citing works
What does inflation really predict?
Tegmark, M. (2005) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2005/04/001 · Cited by 216 · see citing works
Primordial black holes from α-attractors
Dalianis, I., Kehagias, A., & Tringas, G. (2019) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/01/037 · Cited by 213 · see citing works
The evidence for a spatially flat Universe
Efstathiou, G., & Gratton, S. (2020) · Monthly Notices of the Royal Astronomical Society: Letters · doi:10.1093/mnrasl/slaa093 · Cited by 203 · see citing works
Sánchez, A. G., Scóccola, C. G., Ross, A. J., Percival, W. J., Manera, M., Montesano, F., Mazzalay, X., Cuesta, A. J., Eisenstein, D. J., Kazin, E. A., et al. (2012) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2012.21502.x · Cited by 198 · see citing works
Gravitational waves from inflationPreprint
Guzzetti, M. C., Bartolo, N., Liguori, M., & Matarrese, S. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1605.01615 · Cited by 196 · see citing works
Equation-of-state parameter for reheating
Muñoz, J. B., & Kamionkowski, M. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.043521 · Cited by 195 · see citing works
Ballesteros, G., Redondo, J., Ringwald, A., & Tamarit, C. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/08/001 · Cited by 192 · see citing works
Inflationary paradigm after Planck 2013
Guth, A. H., Kaiser, D. I., & Yasunori Nomura, A. (2014) · Physics Letters B · doi:10.1016/j.physletb.2014.03.020 · Cited by 188 · see citing works
Equation of State and Duration to Radiation Domination after Inflation
Lozanov, K. D., & Amin, M. A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.061301 · Cited by 185 · see citing works
Dynamically induced Planck scale and inflation
Kannike, K., Hütsi, G., Pizza, L., Racioppi, A., Raidal, M., Salvio, A., & Струмиа, А. (2015) · Journal of High Energy Physics · doi:10.1007/jhep05(2015)065 · Cited by 172 · see citing works
Cosmological moduli and the post-inflationary universe: A critical review
Kane, G. L., Sinha, K., & Watson, S. (2015) · International Journal of Modern Physics D · doi:10.1142/s0218271815300220 · Cited by 168 · see citing works
Kinney, W. H., Vagnozzi, S., & Visinelli, L. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab1d87 · Cited by 165 · see citing works
Inflaton oscillations and post-inflationary reheating
Garcia, M. A. G., Kaneta, K., Mambrini, Y., & Olive, K. A. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/04/012 · Cited by 165 · see citing works
Unifying Inflation with the Axion, Dark Matter, Baryogenesis, and the Seesaw Mechanism
Ballesteros, G., Redondo, J., Ringwald, A., & Tamarit, C. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.071802 · Cited by 164 · see citing works
Reheating and post-inflationary production of dark matter
García, M. A. G., Kaneta, K., Mambrini, Y., & Olive, K. A. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.123507 · Cited by 162 · see citing works
Inflation and the scale dependent spectral index: prospects and strategies
Adshead, P. J., Easther, R., Pritchard, J. R., & Loeb, A. (2011) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2011/02/021 · Cited by 154 · see citing works
Mechanisms for primordial black hole production in string theory
Özsoy, O., Parameswaran, S., Gianmassimo Tasinato, C., & Ivonne Zavala, C. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/07/005 · Cited by 152 · see citing works
Bayesian analysis of inflation. II. Model selection and constraints on reheating
Easther, R., & Peiris, H. V. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.103533 · Cited by 140 · see citing works
Inflation models and observation
Alabidi, L., & Lyth, D. H. (2006) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2006/05/016 · Cited by 139 · see citing works
Constraining slow-roll inflation with WMAP and 2dF
Leach, S. M., & Liddle, A. R. (2003) · Physical Review D · doi:10.1103/physrevd.68.123508 · Cited by 135 · see citing works
Self-citationMixed inflaton and curvaton perturbations
Langlois, D., & Vernizzi, F. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.063522 · Cited by 123 · see citing works
Calculations of inflaton decays and reheating: with applications to no-scale inflation models
Ellis, J. R., García, M. A. G., Nanopoulos, D. V., & Olive, K. A. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/07/050 · Cited by 120 · see citing works
Tachyon inflation: Tests and comparison with single scalar field inflation
Steer, D. A., & Vernizzi, F. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.043527 · Cited by 120 · see citing works
Considerations in optimizing CMB polarization experiments to constrain inflationary physics
Verde, L., Peiris, H. V., & Jiménez, R. (2006) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2006/01/019 · Cited by 113 · see citing works
Prospects for direct detection of primordial gravitational waves
Chongchitnan, S., & Efstathiou, G. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.083511 · Cited by 113 · see citing works
Observable induced gravitational waves from an early matter phase
Alabidi, L., Kohri, K., Sasaki, M., & Sendouda, Y. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/05/033 · Cited by 116 · see citing works
Cosmological Aspects of Higgs Vacuum Metastability
Markkanen, T., Rajantie, A. K., & Stopyra, S. (2018) · Frontiers in Astronomy and Space Sciences · doi:10.3389/fspas.2018.00040 · Cited by 107 · see citing works
Primordial perturbation in Hořava–Lifshitz cosmology
Yun-song Piao, A. (2009) · Physics Letters B · doi:10.1016/j.physletb.2009.09.047 · Cited by 107 · see citing works
Natural inflation: consistency with cosmic microwave background observations of Planck and BICEP2
Katherine Freese, B., & Kinney, W. H. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/03/044 · Cited by 106 · see citing works
Detailed analysis of the predictions of loop quantum cosmology for the primordial power spectra
Agulló, I., & Morris, N. A. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.124040 · Cited by 106 · see citing works
Planck constraints on single-field inflation
Tsujikawa, S., Ohashi, J., Kuroyanagi, S., & Felice, A. D. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.023529 · Cited by 105 · see citing works
Reheating in R2 Palatini inflationary models
Gialamas, I. D., & Lahanas, A. B. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.084007 · Cited by 103 · see citing works
Bayesian analysis of inflation: Parameter estimation for single field models
Mortonson, M. J., Peiris, H. V., & Easther, R. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.043505 · Cited by 102 · see citing works
Inflation models and observation
Alabidi, L., & Lyth, D. H. (2006) · Lancaster EPrints (Lancaster University) · Cited by 101 · see citing works
Inflation and Cosmological Perturbations
Langlois, D. (2010) · Lecture notes in physics · doi:10.1007/978-3-642-10598-2_1 · Cited by 99 · see citing works
A-term inflation and the smallness of the neutrino masses
Allahverdi, R., Kusenko, A., & Mazumdar, A. (2007) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2007/07/018 · Cited by 98 · see citing works
Running spectral index and formation of primordial black hole in single field inflation models
Drees, M., & Erfani, E. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/01/035 · Cited by 96 · see citing works
Ferreira, R. Z., Jain, R. K., & Sloth, M. S. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/06/053 · Cited by 95 · see citing works
Multiple inflation, cosmic string networks and the string landscape
Burgess, C. P., Easther, R., Mazumdar, A., Mota, D. F., & Multamäki, T. (2005) · Journal of High Energy Physics · doi:10.1088/1126-6708/2005/05/067 · Cited by 95 · see citing works
TeV scale leptogenesis, inflaton dark matter, and neutrino mass in a scotogenic model
Borah, D., Dev, P. S. B., & Kumar, A. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.055012 · Cited by 92 · see citing works
Effective field theories and inflation
Burgess, C. P., Cline, J. M., & Holman, R. (2003) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2003/10/004 · Cited by 92 · see citing works
Nonthermal production of dark matter from primordial black holes
Allahverdi, R., Dent, J. B., & Osiński, J. K. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.055013 · Cited by 89 · see citing works
Multifield dynamics of Higgs inflation
Greenwood, R., Kaiser, D. I., & Sfakianakis, E. I. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.064021 · Cited by 89 · see citing works
Chaotic inflation in modified gravitational theories
Felice, A. D., Tsujikawa, S., Elliston, J., & Tavakol, R. (2011) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2011/08/021 · Cited by 89 · see citing works
Cosmological Aspects of Higgs Vacuum Metastability
Markkanen, T., Rajantie, A., & Stopyra, S. (2018) · UCL Discovery (University College London) · Cited by 87 · see citing works
Unifying Inflation and Dark Matter with Neutrino Masses
Allahverdi, R., Dutta, B., & Mazumdar, A. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.261301 · Cited by 86 · see citing works
D -Term Inflation without Cosmic Strings
Urrestilla, J., Achúcarro, A., & Davis, A.-C. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.251302 · Cited by 84 · see citing works
Minimal Higgs inflation with an R2 term in Palatini gravity
Tenkanen, T. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.063528 · Cited by 82 · see citing works
Planck constraints on monodromy inflation
Easther, R., & Flauger, R. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/02/037 · Cited by 81 · see citing works
Misalignment & Co.: (pseudo-)scalar and vector dark matter with curvature couplings
Alonso-Álvarez, G., Hugle, T., & Jaeckel, J. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/02/014 · Cited by 81 · see citing works
Oscillations in the inflaton potential?
Pahud, C., Kamionkowski, M., & Liddle, A. R. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.79.083503 · Cited by 81 · see citing works
Self-citationTracing the high energy theory of gravity: an introduction to Palatini inflation
Tenkanen, T. (2020) · General Relativity and Gravitation · doi:10.1007/s10714-020-02682-2 · Cited by 77 · see citing works
Katherine Freese, B., & Kinney, W. H. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.083512 · Cited by 78 · see citing works
Low & high scale MSSM inflation, gravitational waves and constraints from Planck
Choudhury, S., Mazumdar, A., & Pal, S. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/07/041 · Cited by 77 · see citing works
Martin, J., Ringeval, C., & Vennin, V. (2024) · Physics of the Dark Universe · doi:10.1016/j.dark.2024.101653 · Cited by 77 · see citing works
Delayed reheating and the breakdown of coherent oscillations
Easther, R., Flauger, R., & Gilmore, J. B. (2011) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2011/04/027 · Cited by 76 · see citing works
Observational constraints on patch inflation in noncommutative spacetime
Calcagni, G., & Tsujikawa, S. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.103514 · Cited by 76 · see citing works
Brane inflation and the WMAP data: a Bayesian analysis
Lorenz, L., Martin, J., & Ringeval, C. (2008) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2008/04/001 · Cited by 76 · see citing works
Dynamically induced Planck scale and inflation in the Palatini formulation
Gialamas, I. D., Καράμ, Α., & Racioppi, A. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/11/014 · Cited by 75 · see citing works
Relaxing constraints on inflation models with curvaton
Moroi, T., Takahashi, T., & Toyoda, Y. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.023502 · Cited by 75 · see citing works
Recent Developments in Warm Inflation
Kamali, V., Motaharfar, M., & Ramos, R. O. (2023) · Universe · doi:10.3390/universe9030124 · Cited by 82 · see citing works
Probing reheating with primordial spectrum
Gong, J.-O., Leung, G., & Pi, S. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/05/027 · Cited by 71 · see citing works
Efstathiou, G., & Mack, K. J. (2005) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2005/05/008 · Cited by 71 · see citing works
Hybrid loop quantum cosmology and predictions for the cosmic microwave background
Gomar, L. C., Marugán, G. A. M., de Blas, D. M., & Olmedo, J. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.103528 · Cited by 71 · see citing works
10 Delayed Reheating and the Breakdown of Coherent OscillationsPreprint
Easther, R., Flauger, R., & Gilmore, J. B. (2016) · Cited by 70 · see citing works
Primordial black holes from multifield inflation with nonminimal couplings
Geller, S. R., Qin, W., McDonough, E., & Kaiser, D. I. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.063535 · Cited by 69 · see citing works
Generating primordial black holes via hilltop-type inflation models
Alabidi, L., & Kohri, K. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.063511 · Cited by 69 · see citing works
BICEP/ Keck constraints on attractor models of inflation and reheating
Ellis, J. R., García, M. A. G., Nanopoulos, D. V., Olive, K. A., & Verner, S. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.043504 · Cited by 68 · see citing works
Small scale structure formation in chameleon cosmology
Brax, P., van de Bruck, C., Davis, A.-C., & Green, A. M. (2006) · Physics Letters B · doi:10.1016/j.physletb.2005.12.055 · Cited by 68 · see citing works
Inflation with a quartic potential in the framework of Einstein-Gauss-Bonnet gravity
Pozdeeva, E. O., Gangopadhyay, M. R., Sami, M., TOPORENSKY, A. V., & Vernov, S. Y. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.043525 · Cited by 67 · see citing works
Refined predictions for Starobinsky inflation and post-inflationary constraints in light of ACT
Drees, M., & Xu, Y. (2025) · Physics Letters B · doi:10.1016/j.physletb.2025.139612 · Cited by 67 · see citing works
Inflection point inflation within supersymmetry
Enqvist, K., Mazumdar, A., & Stephens, P. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/06/020 · Cited by 67 · see citing works
Spacetime dynamics of a Higgs vacuum instability during inflation
East, W. E., Kearney, J., Shakya, B., Yoo, H., & Zurek, K. M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.023526 · Cited by 66 · see citing works
The Numerical Treatment of Inflationary Models
Ringeval, C. (2007) · Springer eBooks · doi:10.1007/978-3-540-74353-8_7 · Cited by 66 · see citing works
- Authors
- Liddle, A. R., & Leach, S. M.
- Affiliations
- University of Sussex (GB)
- ORCID
- Liddle, Andrew R.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2003-11-11
- Volume
- 68
- Issue
- 10
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2170963768
- Semantic Scholar
- dbf34123417af83a8161489a5217d455c90e9d1a
- Cited by
- 607
- References
- 31
- Citations by year
- 2026: 32 · 2025: 39 · 2024: 46 · 2023: 31 · 2022: 30 · 2021: 45 · 2020: 48 · 2019: 35 · 2018: 31 · 2017: 25 · 2016: 30 · 2015: 24 · 2014: 24 · 2013: 11 · 2012: 10
- FWCI
- 10.97
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Archive ouverte UNIGE (University of Geneva) (publishedVersion, other-oa)
- arXiv (Cornell University) (acceptedVersion)
- Sussex Research Online (University of Sussex) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Figshare (submittedVersion, cc-by)
- Archive ouverte UNIGE (University of Geneva) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- Leverhulme Trust
- European Commission
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Keywords
- inflation (cosmology), end of inflation, cosmic inflation, Hubble parameter, primordial perturbations
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
