Enhanced power spectra from multi-field inflation
Abstract: We investigate the enhancement of the power spectra large enough to produce primordial black holes in models with multiple scalar fields. We present analytic solutions for the perturbations in the case of constant turns without the need for an effective field theory for the first time and clarify the role of the Hubble friction that has been overlooked previously. We derive the criteria for an arbitrary number of fields that can lead to an exponential amplification of the curvature perturbation on subhorizon scales, while leaving the perturbations stable on superhorizon scales. Finally, we apply our results to a three-field generalization of the "ultra-light'' scenario and show how the presence of field-space torsion can yield distinct observables compared to the two-field case.
- A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,” Phys. Lett. 91B, 99 (1980) [Adv. Ser. Astrophys. Cosmol. 3, 130 (1987)].
- K. Sato, “Cosmological Baryon Number Domain Structure and the First Order Phase Transition of a Vacuum,” Phys. Lett. 99B, 66 (1981) [Adv. Ser. Astrophys. Cosmol. 3, 134 (1987)].
- K. Sato, “First Order Phase Transition of a Vacuum and Expansion of the Universe,” Mon. Not. Roy. Astron. Soc. 195, 467 (1981).
- D. Kazanas, “Dynamics of the Universe and Spontaneous Symmetry Breaking,” Astrophys. J. 241, L59 (1980).
- A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23, 347 (1981) [Adv. Ser. Astrophys. Cosmol. 3, 139 (1987)].
- A. D. Linde, “A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,” Phys. Lett. 108B, 389 (1982) [Adv. Ser. Astrophys. Cosmol. 3, 149 (1987)].
- A. Albrecht and P. J. Steinhardt, “Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,” Phys. Rev. Lett. 48, 1220 (1982) [Adv. Ser. Astrophys. Cosmol. 3, 158 (1987)].
- V. Mukhanov, “Physical Foundations of Cosmology,” Cambridge, UK: Univ. Pr. (2005) 421 p.
- S. Weinberg, “Cosmology,” Oxford, UK: Oxford Univ. Pr. (2008) 593 p.
- D. H. Lyth and A. R. Liddle, “The primordial density perturbation: Cosmology, inflation and the origin of structure,” Cambridge, UK: Cambridge Univ. Pr. (2009) 497 p.
- J. E. Lidsey, A. R. Liddle, E. W. Kolb, E. J. Copeland, T. Barreiro and M. Abney, “Reconstructing the inflation potential : An overview,” Rev. Mod. Phys. 69, 373-410 (1997) [arXiv:astro-ph/9508078 [astro-ph]].
- F. L. Bezrukov and M. Shaposhnikov, “The Standard Model Higgs boson as the inflaton,” Phys. Lett. B 659, 703-706 (2008) [arXiv:0710.3755 [hep-th]].
- B. A. Bassett, S. Tsujikawa and D. Wands, “Inflation dynamics and reheating,” Rev. Mod. Phys. 78, 537-589 (2006) [arXiv:astro-ph/0507632 [astro-ph]].
- D. Wands, “Multiple field inflation,” Lect. Notes Phys. 738, 275-304 (2008) [arXiv:astro-ph/0702187 [astro-ph]].
- D. Langlois, “Lectures on inflation and cosmological perturbations,” Lect. Notes Phys. 800, 1-57 (2010) [arXiv:1001.5259 [astro-ph.CO]].
- J. O. Gong, “Multi-field inflation and cosmological perturbations,” Int. J. Mod. Phys. D 26, no.01, 1740003 (2016) [arXiv:1606.06971 [gr-qc]].
- J. Chluba, J. Hamann and S. P. Patil, “Features and New Physical Scales in Primordial Observables: Theory and Observation,” Int. J. Mod. Phys. D 24, no.10, 1530023 (2015) [arXiv:1505.01834 [astro-ph.CO]].
- Y. Minami and E. Komatsu, “New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Data,” Phys. Rev. Lett. 125, no.22, 221301 (2020) [arXiv:2011.11254 [astro-ph.CO]].
- J. R. Eskilt and E. Komatsu, “Improved constraints on cosmic birefringence from the WMAP and Planck cosmic microwave background polarization data,” Phys. Rev. D 106, no.6, 063503 (2022) [arXiv:2205.13962 [astro-ph.CO]].
- S. M. Carroll, G. B. Field and R. Jackiw, “Limits on a Lorentz and Parity Violating Modification of Electrodynamics,” Phys. Rev. D 41, 1231 (1990).
- A. G. Riess, S. Casertano, W. Yuan, L. M. Macri and D. Scolnic, “Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM,” Astrophys. J. 876, no.1, 85 (2019) [arXiv:1903.07603 [astro-ph.CO]].
- V. Poulin, T. L. Smith, T. Karwal and M. Kamionkowski, “Early Dark Energy Can Resolve The Hubble Tension,” Phys. Rev. Lett. 122, no.22, 221301 (2019) [arXiv:1811.04083 [astro-ph.CO]].
- Y. B. Zel’dovich and I. D. Novikov, “The Hypothesis of Cores Retarded during Expansion and the Hot Cosmological Model,” Soviet Astron. AJ (Engl. Transl. ), 10, 602 (1967).
- S. Hawking, “Gravitationally collapsed objects of very low mass,” Mon. Not. Roy. Astron. Soc. 152, 75 (1971).
- B. J. Carr and S. W. Hawking, “Black holes in the early Universe,” Mon. Not. Roy. Astron. Soc. 168, 399-415 (1974).
- T. Harada, C. M. Yoo and K. Kohri, “Threshold of primordial black hole formation,” Phys. Rev. D 88, no.8, 084051 (2013) [erratum: Phys. Rev. D 89, no.2, 029903 (2014)] [arXiv:1309.4201 [astro-ph.CO]].
- C. T. Byrnes, P. S. Cole and S. P. Patil, “Steepest growth of the power spectrum and primordial black holes,” JCAP 06, 028 (2019) [arXiv:1811.11158 [astro-ph.CO]].
- P. Carrilho, K. A. Malik and D. J. Mulryne, “Dissecting the growth of the power spectrum for primordial black holes,” Phys. Rev. D 100 (2019) no.10, 103529 [arXiv:1907.05237 [astro-ph.CO]].
- S. Pi, Y. l. Zhang, Q. G. Huang and M. Sasaki, “Scalaron from R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-gravity as a heavy field,” JCAP 05, 042 (2018) [arXiv:1712.09896 [astro-ph.CO]].
- J. Garcia-Bellido, A. D. Linde and D. Wands, “Density perturbations and black hole formation in hybrid inflation,” Phys. Rev. D 54 (1996), 6040-6058 [arXiv:astro-ph/9605094 [astro-ph]].
- D. Y. Cheong, S. M. Lee and S. C. Park, “Primordial black holes in Higgs-R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT inflation as the whole of dark matter,” JCAP 01 (2021), 032 [arXiv:1912.12032 [hep-ph]].
- M. Braglia, D. K. Hazra, F. Finelli, G. F. Smoot, L. Sriramkumar and A. A. Starobinsky, “Generating PBHs and small-scale GWs in two-field models of inflation,” JCAP 08 (2020), 001 [arXiv:2005.02895 [astro-ph.CO]].
- M. Braglia, A. Linde, R. Kallosh and F. Finelli, “Hybrid α𝛼\alphaitalic_α-attractors, primordial black holes and gravitational wave backgrounds,” JCAP 04 (2023), 033 [arXiv:2211.14262 [astro-ph.CO]].
- D. Y. Cheong, K. Kohri and S. C. Park, “The inflaton that could: primordial black holes and second order gravitational waves from tachyonic instability induced in Higgs-R 22{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT inflation,” JCAP 10 (2022), 015 [arXiv:2205.14813 [hep-ph]].
- G. A. Palma, S. Sypsas and C. Zenteno, “Seeding primordial black holes in multifield inflation,” Phys. Rev. Lett. 125, no.12, 121301 (2020) [arXiv:2004.06106 [astro-ph.CO]].
- J. Fumagalli, S. Renaux-Petel and L. T. Witkowski, “Oscillations in the stochastic gravitational wave background from sharp features and particle production during inflation,” JCAP 08 (2021), 030 [arXiv:2012.02761 [astro-ph.CO]].
- J. Fumagalli, S. Renaux-Petel, J. W. Ronayne and L. T. Witkowski, “Turning in the landscape: A new mechanism for generating primordial black holes,” Phys. Lett. B 841 (2023), 137921 [arXiv:2004.08369 [hep-th]].
- E. W. Kolb, A. J. Long, E. McDonough and G. Payeur, “Completely dark matter from rapid-turn multifield inflation,” JHEP 02 (2023), 181 [arXiv:2211.14323 [hep-th]].
- L. Anguelova, “On Primordial Black Holes from Rapid Turns in Two-field Models,” JCAP 06 (2021), 004 [arXiv:2012.03705 [hep-th]].
- S. Bhattacharya and I. Zavala, “Sharp turns in axion monodromy: primordial black holes and gravitational waves,” JCAP 04 (2023), 065 [arXiv:2205.06065 [astro-ph.CO]].
- J. Fumagalli, G. A. Palma, S. Renaux-Petel, S. Sypsas, L. T. Witkowski and C. Zenteno, “Primordial gravitational waves from excited states,” JHEP 03 (2022), 196 [arXiv:2111.14664 [astro-ph.CO]].
- V. Aragam, S. Paban and R. Rosati, “Primordial stochastic gravitational wave backgrounds from a sharp feature in three-field inflation. Part I. The radiation era,” JCAP 11 (2023), 014 [arXiv:2304.00065 [astro-ph.CO]].
- Y. F. Cai, X. Tong, D. G. Wang and S. F. Yan, “Primordial Black Holes from Sound Speed Resonance during Inflation,” Phys. Rev. Lett. 121, no.8, 081306 (2018) [arXiv:1805.03639 [astro-ph.CO]].
- K. Boutivas, I. Dalianis, G. P. Kodaxis and N. Tetradis, “The effect of multiple features on the power spectrum in two-field inflation,” JCAP 08 (2022) no.08, 021 [arXiv:2203.15605 [astro-ph.CO]].
- A. Achucarro, J. O. Gong, S. Hardeman, G. A. Palma and S. P. Patil, “Features of heavy physics in the CMB power spectrum,” JCAP 01 (2011), 030 [arXiv:1010.3693 [hep-ph]].
- C. Gordon, D. Wands, B. A. Bassett and R. Maartens, “Adiabatic and entropy perturbations from inflation,” Phys. Rev. D 63 (2000), 023506 [arXiv:astro-ph/0009131 [astro-ph]].
- A. Achucarro, J. O. Gong, S. Hardeman, G. A. Palma and S. P. Patil, “Effective theories of single field inflation when heavy fields matter,” JHEP 05 (2012), 066 [arXiv:1201.6342 [hep-th]].
- E. Kreyszig, “Differential Geometry”, Dover Publications, 2013.
- A. Achúcarro, S. Céspedes, A. C. Davis and G. A. Palma, “Constraints on Holographic Multifield Inflation and Models Based on the Hamilton-Jacobi Formalism,” Phys. Rev. Lett. 122 (2019) no.19, 191301 [arXiv:1809.05341 [hep-th]].
- L. Pinol, “Multifield inflation beyond Nfield=2subscript𝑁field2N_{\mathrm{field}}=2italic_N start_POSTSUBSCRIPT roman_field end_POSTSUBSCRIPT = 2: non-Gaussianities and single-field effective theory,” JCAP 04 (2021), 002 [arXiv:2011.05930 [astro-ph.CO]].
- Z. Lalak, D. Langlois, S. Pokorski and K. Turzynski, “Curvature and isocurvature perturbations in two-field inflation,” JCAP 07 (2007), 014 [arXiv:0704.0212 [hep-th]].
- S. Cremonini, Z. Lalak and K. Turzynski, “Strongly Coupled Perturbations in Two-Field Inflationary Models,” JCAP 03 (2011), 016 [arXiv:1010.3021 [hep-th]].
- J. O. Gong and E. D. Stewart, “The Density perturbation power spectrum to second order corrections in the slow roll expansion,” Phys. Lett. B 510, 1-9 (2001) [arXiv:astro-ph/0101225 [astro-ph]].
- E. D. Stewart and D. H. Lyth, “A More accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation,” Phys. Lett. B 302 (1993), 171-175 [arXiv:gr-qc/9302019 [gr-qc]].
- T. Bjorkmo, R. Z. Ferreira and M. C. D. Marsh, “Mild Non-Gaussianities under Perturbative Control from Rapid-Turn Inflation Models,” JCAP 12 (2019), 036 [arXiv:1908.11316 [hep-th]].
- S. Garcia-Saenz and S. Renaux-Petel, “Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of sound,” JCAP 11 (2018), 005 [arXiv:1805.12563 [hep-th]].
- A. Achucarro, V. Atal, S. Cespedes, J. O. Gong, G. A. Palma and S. P. Patil, “Heavy fields, reduced speeds of sound and decoupling during inflation,” Phys. Rev. D 86 (2012), 121301 [arXiv:1205.0710 [hep-th]].
- T. Kato, “On the Adiabatic Theorem of Quantum Mechanics,” Journal of the Physical Society of Japan 5, 435 (1950),
- S. Blanes, F. Casas, J. A. Oteo and J. Ros, “The Magnus expansion and some of its applications,” Phys. Rept. 470 (2009), 151-238
- M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Roy. Soc. Lond. A 392 (1984), 45-57
- Y. S. Barkovsky, “Lectures on the Routh-Hurwitz problem,” [arXiv:0802.1805 [math.CA]].
- N. Levinson, “The asymptotic nature of solutions of linear systems of differential equations,” Duke Math. J. 15 (1) 111 - 126, March 1948.
- P. Christodoulidis and R. Rosati, “(Slow-)twisting inflationary attractors,” JCAP 09 (2023), 034 [arXiv:2210.14900 [hep-th]].
- A. Achúcarro, V. Atal, C. Germani and G. A. Palma, “Cumulative effects in inflation with ultra-light entropy modes,” JCAP 02 (2017), 013 [arXiv:1607.08609 [astro-ph.CO]].
- P. Christodoulidis, D. Roest and E. I. Sfakianakis, “Attractors, Bifurcations and Curvature in Multi-field Inflation,” JCAP 08 (2020), 006 [arXiv:1903.03513 [gr-qc]].
- A. Achúcarro, E. J. Copeland, O. Iarygina, G. A. Palma, D. G. Wang and Y. Welling, “Shift-symmetric orbital inflation: Single field or multifield?,” Phys. Rev. D 102 (2020) no.2, 021302 [arXiv:1901.03657 [astro-ph.CO]].
- V. Aragam, S. Paban and R. Rosati, “Multi-field Inflation in High-Slope Potentials,” JCAP 04 (2020), 022 [arXiv:1905.07495 [hep-th]].
- M. Sasaki, “Large Scale Quantum Fluctuations in the Inflationary Universe,” Prog. Theor. Phys. 76 (1986), 1036
- V. F. Mukhanov, “Quantum Theory of Gauge Invariant Cosmological Perturbations,” Sov. Phys. JETP 67 (1988), 1297-1302
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.