Papers
Topics
Authors
Recent
Search
2000 character limit reached

Climbing over the potential barrier during inflation via null energy condition violation

Published 19 Apr 2024 in astro-ph.CO, gr-qc, and hep-th | (2404.12655v2)

Abstract: The violation of the null energy condition (NEC) may play a crucial role in enabling a scalar field to climb over high potential barriers, potentially significant in the very early universe. We propose a single-field model where the universe sequentially undergoes a first stage of slow-roll inflation, NEC violation, and a second stage of slow-roll inflation. Through the NEC violation, the scalar field climbs over high potential barriers, leaving unique characteristics on the primordial gravitational wave power spectrum, including a blue-tilted nature in the middle-frequency range and diminishing oscillation amplitudes at higher frequencies. Additionally, the power spectrum exhibits nearly scale-invariant behavior on both large and small scales.

Authors (3)
Definition Search Book Streamline Icon: https://streamlinehq.com
References (106)
  1. S. L. Detweiler, “Pulsar timing measurements and the search for gravitational waves,” Astrophys. J. 234 (1979) 1100–1104.
  2. LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett. 116 no. 6, (2016) 061102, arXiv:1602.03837 [gr-qc].
  3. NANOGrav Collaboration, G. Agazie et al., “The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background,” Astrophys. J. Lett. 951 no. 1, (2023) L8, arXiv:2306.16213 [astro-ph.HE].
  4. NANOGrav Collaboration, A. Afzal et al., “The NANOGrav 15 yr Data Set: Search for Signals from New Physics,” Astrophys. J. Lett. 951 no. 1, (2023) L11, arXiv:2306.16219 [astro-ph.HE].
  5. NANOGrav Collaboration, Z. Arzoumanian et al., “The NANOGrav 12.5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background,” Astrophys. J. Lett. 905 no. 2, (2020) L34, arXiv:2009.04496 [astro-ph.HE].
  6. EPTA, InPTA: Collaboration, J. Antoniadis et al., “The second data release from the European Pulsar Timing Array - III. Search for gravitational wave signals,” Astron. Astrophys. 678 (2023) A50, arXiv:2306.16214 [astro-ph.HE].
  7. D. J. Reardon et al., “Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array,” Astrophys. J. Lett. 951 no. 1, (2023) L6, arXiv:2306.16215 [astro-ph.HE].
  8. H. Xu et al., “Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I,” Res. Astron. Astrophys. 23 no. 7, (2023) 075024, arXiv:2306.16216 [astro-ph.HE].
  9. L. P. Grishchuk, “Amplification of gravitational waves in an istropic universe,” Zh. Eksp. Teor. Fiz. 67 (1974) 825–838.
  10. A. A. Starobinsky, “Spectrum of relict gravitational radiation and the early state of the universe,” JETP Lett. 30 (1979) 682–685.
  11. V. A. Rubakov, M. V. Sazhin, and A. V. Veryaskin, “Graviton Creation in the Inflationary Universe and the Grand Unification Scale,” Phys. Lett. B 115 (1982) 189–192.
  12. A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23 (1981) 347–356.
  13. A. D. Linde, “A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,” Phys. Lett. B 108 (1982) 389–393.
  14. A. Albrecht and P. J. Steinhardt, “Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,” Phys. Rev. Lett. 48 (1982) 1220–1223.
  15. A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,” Phys. Lett. B 91 (1980) 99–102.
  16. S. Vagnozzi, “Inflationary interpretation of the stochastic gravitational wave background signal detected by pulsar timing array experiments,” JHEAp 39 (2023) 81–98, arXiv:2306.16912 [astro-ph.CO].
  17. J.-Q. Jiang, Y. Cai, G. Ye, and Y.-S. Piao, “Broken blue-tilted inflationary gravitational waves: a joint analysis of NANOGrav 15-year and BICEP/Keck 2018 data,” arXiv:2307.15547 [astro-ph.CO].
  18. M. Zhu, G. Ye, and Y. Cai, “Pulsar timing array observations as possible hints for nonsingular cosmology,” Eur. Phys. J. C 83 no. 9, (2023) 816, arXiv:2307.16211 [astro-ph.CO].
  19. G. Ye, M. Zhu, and Y. Cai, “Null energy condition violation during inflation and pulsar timing array observations,” JHEP 02 (2024) 008, arXiv:2312.10685 [gr-qc].
  20. L. Frosina and A. Urbano, “Inflationary interpretation of the nHz gravitational-wave background,” Phys. Rev. D 108 no. 10, (2023) 103544, arXiv:2308.06915 [astro-ph.CO].
  21. J. Ellis, M. Fairbairn, G. Franciolini, G. Hütsi, A. Iovino, M. Lewicki, M. Raidal, J. Urrutia, V. Vaskonen, and H. Veermäe, “What is the source of the PTA GW signal?,” Phys. Rev. D 109 no. 2, (2024) 023522, arXiv:2308.08546 [astro-ph.CO].
  22. H.-L. Huang, Y. Cai, J.-Q. Jiang, J. Zhang, and Y.-S. Piao, “Supermassive primordial black holes in multiverse: for nano-Hertz gravitational wave and high-redshift JWST galaxies,” arXiv:2306.17577 [gr-qc].
  23. X. K. Du, M. X. Huang, F. Wang, and Y. K. Zhang, “Did the nHZ Gravitational Waves Signatures Observed By NANOGrav Indicate Multiple Sector SUSY Breaking?,” arXiv:2307.02938 [hep-ph].
  24. Y.-M. Wu, Z.-C. Chen, and Q.-G. Huang, “Cosmological Interpretation for the Stochastic Signal in Pulsar Timing Arrays,” arXiv:2307.03141 [astro-ph.CO].
  25. Y. Xiao, J. M. Yang, and Y. Zhang, “Implications of nano-Hertz gravitational waves on electroweak phase transition in the singlet dark matter model,” Sci. Bull. 68 (2023) 3158–3164, arXiv:2307.01072 [hep-ph].
  26. C. Zhang, N. Dai, Q. Gao, Y. Gong, T. Jiang, and X. Lu, “Detecting new fundamental fields with pulsar timing arrays,” Phys. Rev. D 108 no. 10, (2023) 104069, arXiv:2307.01093 [gr-qc].
  27. G. Ye and A. Silvestri, “Can the Gravitational Wave Background Feel Wiggles in Spacetime?,” Astrophys. J. Lett. 963 no. 1, (2024) L15, arXiv:2307.05455 [astro-ph.CO].
  28. S. F. King, R. Roshan, X. Wang, G. White, and M. Yamazaki, “Quantum gravity effects on dark matter and gravitational waves,” Phys. Rev. D 109 no. 2, (2024) 024057, arXiv:2308.03724 [hep-ph].
  29. M. X. Huang, F. Wang, and Y. K. Zhang, “The Interplay Between the Muon g−2𝑔2g-2italic_g - 2 Anomaly and the PTA nHZ Gravitational Waves from Domain Walls in NMSSM,” arXiv:2309.06378 [hep-ph].
  30. K. D. Lozanov, S. Pi, M. Sasaki, V. Takhistov, and A. Wang, “Axion Universal Gravitational Wave Interpretation of Pulsar Timing Array Data,” arXiv:2310.03594 [astro-ph.CO].
  31. R. Maji and W.-I. Park, “Supersymmetric U(1)B-L flat direction and NANOGrav 15 year data,” JCAP 01 (2024) 015, arXiv:2308.11439 [hep-ph].
  32. M. Kawasaki and K. Murai, “Enhancement of gravitational waves at Q-ball decay including non-linear density perturbations,” JCAP 01 (2024) 050, arXiv:2308.13134 [astro-ph.CO].
  33. S. He, L. Li, S. Wang, and S.-J. Wang, “Constraints on holographic QCD phase transitions from PTA observations,” arXiv:2308.07257 [hep-ph].
  34. S. Choudhury, K. Dey, A. Karde, S. Panda, and M. Sami, “Primordial non-Gaussianity as a saviour for PBH overproduction in SIGWs generated by Pulsar Timing Arrays for Galileon inflation,” arXiv:2310.11034 [astro-ph.CO].
  35. S. Choudhury, K. Dey, and A. Karde, “Untangling PBH overproduction in w𝑤witalic_w-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation,” arXiv:2311.15065 [astro-ph.CO].
  36. J.-Q. Jiang and Y.-S. Piao, “Search for the non-linearities of gravitational wave background in NANOGrav 15-year data set,” arXiv:2401.16950 [gr-qc].
  37. M. De Angelis, A. Smith, W. Giarè, and C. van de Bruck, “Gravitational waves in a cyclic Universe: resilience through cycles and vacuum state,” arXiv:2403.00533 [hep-th].
  38. BICEP, Keck Collaboration, P. A. R. Ade et al., “Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,” Phys. Rev. Lett. 127 no. 15, (2021) 151301, arXiv:2110.00483 [astro-ph.CO].
  39. D. Borah, S. Jyoti Das, and R. Samanta, “Imprint of inflationary gravitational waves and WIMP dark matter in pulsar timing array data,” arXiv:2307.00537 [hep-ph].
  40. S. Choudhury, “Single field inflation in the light of Pulsar Timing Array Data: Quintessential interpretation of blue tilted tensor spectrum through Non-Bunch Davies initial condition,” arXiv:2307.03249 [astro-ph.CO].
  41. I. Ben-Dayan, U. Kumar, U. Thattarampilly, and A. Verma, “Probing the early Universe cosmology with NANOGrav: Possibilities and limitations,” Phys. Rev. D 108 no. 10, (2023) 103507, arXiv:2307.15123 [astro-ph.CO].
  42. V. K. Oikonomou, “Flat energy spectrum of primordial gravitational waves versus peaks and the NANOGrav 2023 observation,” Phys. Rev. D 108 no. 4, (2023) 043516, arXiv:2306.17351 [astro-ph.CO].
  43. S. Datta, “Explaining PTA Data with Inflationary GWs in a PBH-Dominated Universe,” arXiv:2309.14238 [hep-ph].
  44. Y.-S. Piao and Y.-Z. Zhang, “Phantom inflation and primordial perturbation spectrum,” Phys. Rev. D 70 (2004) 063513, arXiv:astro-ph/0401231.
  45. M. Baldi, F. Finelli, and S. Matarrese, “Inflation with violation of the null energy condition,” Phys. Rev. D 72 (2005) 083504, arXiv:astro-ph/0505552.
  46. Y.-S. Piao, “Gravitational wave background from phantom superinflation,” Phys. Rev. D 73 (2006) 047302, arXiv:gr-qc/0601115.
  47. T. Kobayashi, M. Yamaguchi, and J. Yokoyama, “G-inflation: Inflation driven by the Galileon field,” Phys. Rev. Lett. 105 (2010) 231302, arXiv:1008.0603 [hep-th].
  48. T. Kobayashi, M. Yamaguchi, and J. Yokoyama, “Generalized G-inflation: Inflation with the most general second-order field equations,” Prog. Theor. Phys. 126 (2011) 511–529, arXiv:1105.5723 [hep-th].
  49. S. Endlich, A. Nicolis, and J. Wang, “Solid Inflation,” JCAP 10 (2013) 011, arXiv:1210.0569 [hep-th].
  50. Y.-F. Cai, J.-O. Gong, S. Pi, E. N. Saridakis, and S.-Y. Wu, “On the possibility of blue tensor spectrum within single field inflation,” Nucl. Phys. B 900 (2015) 517–532, arXiv:1412.7241 [hep-th].
  51. J.-O. Gong, “Blue running of the primordial tensor spectrum,” JCAP 07 (2014) 022, arXiv:1403.5163 [astro-ph.CO].
  52. D. Cannone, G. Tasinato, and D. Wands, “Generalised tensor fluctuations and inflation,” JCAP 01 (2015) 029, arXiv:1409.6568 [astro-ph.CO].
  53. Y. Wang and W. Xue, “Inflation and Alternatives with Blue Tensor Spectra,” JCAP 10 (2014) 075, arXiv:1403.5817 [astro-ph.CO].
  54. S. Kuroyanagi, T. Takahashi, and S. Yokoyama, “Blue-tilted Tensor Spectrum and Thermal History of the Universe,” JCAP 02 (2015) 003, arXiv:1407.4785 [astro-ph.CO].
  55. Y. Cai, Y.-T. Wang, and Y.-S. Piao, “Is there an effect of a nontrivial cTsubscript𝑐𝑇c_{T}italic_c start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT during inflation?,” Phys. Rev. D 93 no. 6, (2016) 063005, arXiv:1510.08716 [astro-ph.CO].
  56. Y. Cai, Y.-T. Wang, and Y.-S. Piao, “Propagating speed of primordial gravitational waves and inflation,” Phys. Rev. D 94 no. 4, (2016) 043002, arXiv:1602.05431 [astro-ph.CO].
  57. Y.-T. Wang, Y. Cai, Z.-G. Liu, and Y.-S. Piao, “Probing the primordial universe with gravitational waves detectors,” JCAP 01 (2017) 010, arXiv:1612.05088 [astro-ph.CO].
  58. T. Fujita, S. Kuroyanagi, S. Mizuno, and S. Mukohyama, “Blue-tilted Primordial Gravitational Waves from Massive Gravity,” Phys. Lett. B 789 (2019) 215–219, arXiv:1808.02381 [gr-qc].
  59. S. Kuroyanagi, T. Takahashi, and S. Yokoyama, “Blue-tilted inflationary tensor spectrum and reheating in the light of NANOGrav results,” JCAP 01 (2021) 071, arXiv:2011.03323 [astro-ph.CO].
  60. S. Akama, S. Hirano, and T. Kobayashi, “Primordial tensor non-Gaussianities from general single-field inflation with non-Bunch-Davies initial states,” Phys. Rev. D 102 no. 2, (2020) 023513, arXiv:2003.10686 [gr-qc].
  61. S. Akama and H. W. H. Tahara, “Imprints of primordial gravitational waves with non-Bunch-Davies initial states on CMB bispectra,” Phys. Rev. D 108 no. 10, (2023) 103522, arXiv:2306.17752 [gr-qc].
  62. W. Giarè, F. Renzi, and A. Melchiorri, “Higher-Curvature Corrections and Tensor Modes,” Phys. Rev. D 103 no. 4, (2021) 043515, arXiv:2012.00527 [astro-ph.CO].
  63. W. Giarè, M. Forconi, E. Di Valentino, and A. Melchiorri, “Towards a reliable calculation of relic radiation from primordial gravitational waves,” Mon. Not. Roy. Astron. Soc. 520 (2023) 2, arXiv:2210.14159 [astro-ph.CO].
  64. V. K. Oikonomou, “A Stiff Pre-CMB Era with a Mildly Blue-tilted Tensor Inflationary Era can Explain the 2023 NANOGrav Signal,” arXiv:2309.04850 [astro-ph.CO].
  65. V. K. Oikonomou, P. Tsyba, and O. Razina, “Red or blue tensor spectrum from GW170817-compatible Einstein-Gauss-Bonnet theory: A detailed analysis,” EPL 145 no. 4, (2024) 49001, arXiv:2402.02049 [gr-qc].
  66. V. Rubakov, “The Null Energy Condition and its violation,” Usp. Fiz. Nauk 184 no. 2, (2014) 137–152, arXiv:1401.4024 [hep-th].
  67. M. Libanov, S. Mironov, and V. Rubakov, “Generalized Galileons: instabilities of bouncing and Genesis cosmologies and modified Genesis,” JCAP 08 (2016) 037, arXiv:1605.05992 [hep-th].
  68. T. Kobayashi, “Generic instabilities of nonsingular cosmologies in Horndeski theory: A no-go theorem,” Phys. Rev. D 94 no. 4, (2016) 043511, arXiv:1606.05831 [hep-th].
  69. D. A. Easson, I. Sawicki, and A. Vikman, “G-Bounce,” JCAP 11 (2011) 021, arXiv:1109.1047 [hep-th].
  70. T. Qiu and Y.-T. Wang, “G-Bounce Inflation: Towards Nonsingular Inflation Cosmology with Galileon Field,” JHEP 04 (2015) 130, arXiv:1501.03568 [astro-ph.CO].
  71. A. Ijjas and P. J. Steinhardt, “Classically stable nonsingular cosmological bounces,” Phys. Rev. Lett. 117 no. 12, (2016) 121304, arXiv:1606.08880 [gr-qc].
  72. A. Ijjas and P. J. Steinhardt, “Fully stable cosmological solutions with a non-singular classical bounce,” Phys. Lett. B 764 (2017) 289–294, arXiv:1609.01253 [gr-qc].
  73. D. A. Dobre, A. V. Frolov, J. T. Gálvez Ghersi, S. Ramazanov, and A. Vikman, “Unbraiding the Bounce: Superluminality around the Corner,” JCAP 03 (2018) 020, arXiv:1712.10272 [gr-qc].
  74. Y. Cai, Y. Wan, H.-G. Li, T. Qiu, and Y.-S. Piao, “The Effective Field Theory of nonsingular cosmology,” JHEP 01 (2017) 090, arXiv:1610.03400 [gr-qc].
  75. P. Creminelli, D. Pirtskhalava, L. Santoni, and E. Trincherini, “Stability of Geodesically Complete Cosmologies,” JCAP 11 (2016) 047, arXiv:1610.04207 [hep-th].
  76. Y. Cai, H.-G. Li, T. Qiu, and Y.-S. Piao, “The Effective Field Theory of nonsingular cosmology: II,” Eur. Phys. J. C 77 no. 6, (2017) 369, arXiv:1701.04330 [gr-qc].
  77. Y. Cai and Y.-S. Piao, “A covariant Lagrangian for stable nonsingular bounce,” JHEP 09 (2017) 027, arXiv:1705.03401 [gr-qc].
  78. R. Kolevatov, S. Mironov, N. Sukhov, and V. Volkova, “Cosmological bounce and Genesis beyond Horndeski,” JCAP 08 (2017) 038, arXiv:1705.06626 [hep-th].
  79. Y. Cai and Y.-S. Piao, “Higher order derivative coupling to gravity and its cosmological implications,” Phys. Rev. D 96 no. 12, (2017) 124028, arXiv:1707.01017 [gr-qc].
  80. Y. Cai, Y.-T. Wang, J.-Y. Zhao, and Y.-S. Piao, “Primordial perturbations with pre-inflationary bounce,” Phys. Rev. D 97 no. 10, (2018) 103535, arXiv:1709.07464 [astro-ph.CO].
  81. S. Mironov, V. Rubakov, and V. Volkova, “Bounce beyond Horndeski with GR asymptotics and γ𝛾\gammaitalic_γ-crossing,” JCAP 10 (2018) 050, arXiv:1807.08361 [hep-th].
  82. T. Qiu, K. Tian, and S. Bu, “Perturbations of bounce inflation scenario from f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) modified gravity revisited,” Eur. Phys. J. C 79 no. 3, (2019) 261, arXiv:1810.04436 [gr-qc].
  83. G. Ye and Y.-S. Piao, “Implication of GW170817 for cosmological bounces,” Commun. Theor. Phys. 71 no. 4, (2019) 427, arXiv:1901.02202 [gr-qc].
  84. G. Ye and Y.-S. Piao, “Bounce in general relativity and higher-order derivative operators,” Phys. Rev. D 99 no. 8, (2019) 084019, arXiv:1901.08283 [gr-qc].
  85. S. Mironov, V. Rubakov, and V. Volkova, “Genesis with general relativity asymptotics in beyond Horndeski theory,” Phys. Rev. D 100 no. 8, (2019) 083521, arXiv:1905.06249 [hep-th].
  86. S. Akama, S. Hirano, and T. Kobayashi, “Primordial non-Gaussianities of scalar and tensor perturbations in general bounce cosmology: Evading the no-go theorem,” Phys. Rev. D 101 no. 4, (2020) 043529, arXiv:1908.10663 [gr-qc].
  87. S. Mironov, V. Rubakov, and V. Volkova, “Subluminal cosmological bounce beyond Horndeski,” JCAP 05 (2020) 024, arXiv:1910.07019 [hep-th].
  88. A. Ilyas, M. Zhu, Y. Zheng, Y.-F. Cai, and E. N. Saridakis, “DHOST Bounce,” JCAP 09 (2020) 002, arXiv:2002.08269 [gr-qc].
  89. A. Ilyas, M. Zhu, Y. Zheng, and Y.-F. Cai, “Emergent Universe and Genesis from the DHOST Cosmology,” JHEP 01 (2021) 141, arXiv:2009.10351 [gr-qc].
  90. M. Zhu, A. Ilyas, Y. Zheng, Y.-F. Cai, and E. N. Saridakis, “Scalar and tensor perturbations in DHOST bounce cosmology,” JCAP 11 no. 11, (2021) 045, arXiv:2108.01339 [gr-qc].
  91. M. Zhu and Y. Zheng, “Improved DHOST Genesis,” JHEP 11 (2021) 163, arXiv:2109.05277 [gr-qc].
  92. S. Mironov and V. Volkova, “Stable nonsingular cosmologies in beyond Horndeski theory and disformal transformations,” Int. J. Mod. Phys. A 37 no. 14, (2022) 2250088, arXiv:2204.05889 [hep-th].
  93. Y. Cai, J. Xu, S. Zhao, and S. Zhou, “Perturbative unitarity and NEC violation in genesis cosmology,” JHEP 10 (2022) 140, arXiv:2207.11772 [gr-qc]. [Erratum: JHEP 11, 063 (2022)].
  94. A. Panda, D. Gangopadhyay, and G. Manna, “NEC violation in f⁢(R¯,T¯)𝑓¯𝑅¯𝑇f(\bar{R},\bar{T})italic_f ( over¯ start_ARG italic_R end_ARG , over¯ start_ARG italic_T end_ARG ) gravity in the context of a non-canonical theory via modified Raychaudhuri equation,” arXiv:2402.18431 [gr-qc].
  95. Y. Cai and Y.-S. Piao, “Intermittent null energy condition violations during inflation and primordial gravitational waves,” Phys. Rev. D 103 no. 8, (2021) 083521, arXiv:2012.11304 [gr-qc].
  96. Y. Cai and Y.-S. Piao, “Generating enhanced primordial GWs during inflation with intermittent violation of NEC and diminishment of GW propagating speed,” JHEP 06 (2022) 067, arXiv:2201.04552 [gr-qc].
  97. Z.-C. Chen and L. Liu, “Constraints on Null Energy Condition Violation from Advanced LIGO and Advanced Virgo’s First Three Observing Runs,” arXiv:2404.07075 [gr-qc].
  98. Z.-C. Chen and L. Liu, “Detecting a Gravitational-Wave Background from Null Energy Condition Violation: Prospects for Taiji,” arXiv:2404.08375 [gr-qc].
  99. Y. Cai, M. Zhu, and Y.-S. Piao, “Primordial black holes from null energy condition violation during inflation,” arXiv:2305.10933 [gr-qc].
  100. Y. Cai, “Generating enhanced parity-violating gravitational waves during inflation with violation of the null energy condition,” Phys. Rev. D 107 no. 6, (2023) 063512, arXiv:2212.10893 [gr-qc].
  101. M. Zhu and Y. Cai, “Parity-violation in bouncing cosmology,” JHEP 04 (2023) 095, arXiv:2301.13502 [gr-qc].
  102. Y. Cai, Y.-T. Wang, and Y.-S. Piao, “Preinflationary primordial perturbations,” Phys. Rev. D 92 no. 2, (2015) 023518, arXiv:1501.01730 [astro-ph.CO].
  103. Y. Cai and Y.-S. Piao, “Pre-inflation and trans-Planckian censorship,” Sci. China Phys. Mech. Astron. 63 no. 11, (2020) 110411, arXiv:1909.12719 [gr-qc].
  104. M. S. Turner, M. J. White, and J. E. Lidsey, “Tensor perturbations in inflationary models as a probe of cosmology,” Phys. Rev. D 48 (1993) 4613–4622, arXiv:astro-ph/9306029.
  105. L. A. Boyle and P. J. Steinhardt, “Probing the early universe with inflationary gravitational waves,” Phys. Rev. D 77 (2008) 063504, arXiv:astro-ph/0512014.
  106. W. Zhao and Y. Zhang, “Relic gravitational waves and their detection,” Phys. Rev. D 74 (2006) 043503, arXiv:astro-ph/0604458.
Citations (3)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Tweets

Sign up for free to view the 1 tweet with 1 like about this paper.

Sign Up for Free