The paper introduces new exponential and polynomial supergravity ξ-attractor models in the Jordan frame with non-minimal coupling and shows that Palatini gravity with independent affine connection has no supergravity embedding.
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The Unity of Cosmological Attractors
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abstract
Recently, several broad classes of inflationary models have been discovered whose cosmological predictions are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a non-minimal coupling to gravity. These models, which we will call $\xi$-attractors, describe universal cosmological attractors (including Higgs inflation) and induced inflation models. Another class describes conformal attractors (including Starobinsky inflation and T-models) and their generalization to $\alpha$-attractors. The aim of this paper is to elucidate the common denominator of these models: their attractor properties stem from a pole of order two in the kinetic term of the inflaton field in the Einstein frame formulation, prior to switching to the canonical variables. We point out that $\alpha$- and universal attractors differ in the subleading corrections to the kinetic term. As a final step towards unification of $\xi$ and $\alpha$ attractors, we introduce a special class of $\xi$-attractors which is fully equivalent to $\alpha$-attractors with the identification $\alpha = 1+{1\over 6\xi}$. There is no theoretical lower bound on $r$ in this class of models.
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Non-minimal coupling of the inflaton to the Holst invariant in metric-affine gravity induces quasi-pole kinetics that generate an exponential plateau potential and Starobinsky-equivalent predictions regardless of the bare potential.
Nonminimal derivative coupling realizes the Harrison-Zeldovich attractor for monomial, hilltop, and α-attractor E-models, pulling them to the scale-invariant spectrum suggested by ACT data.
Inflaton accretion during reheating drives non-linear PBH mass growth that extends lifetimes and amplifies emitted SGWB by multiple orders of magnitude.
New ξ-attractors with non-minimal coupling and non-canonical kinetics yield Einstein-frame exponential and polynomial potentials whose ns spans 1-2/N to 1-1/N and r can reach zero as ξ grows, fitting Planck, BICEP/Keck, ACT, SPT, and DESI data, plus a supergravity realization.
High-frequency primordial gravitational waves extend to higher frequencies due to post-inflation inflaton dynamics, and their detailed spectrum shape can distinguish inflation models.
Polynomial α-attractor P-models of inflation accommodate Planck and Planck+ACT CMB data for ranges of reheating temperatures when decays and fragmentation are included.
Final Planck CMB data confirms the flat 6-parameter ΛCDM model with Ω_c h² = 0.120 ± 0.001, Ω_b h² = 0.0224 ± 0.0001, n_s = 0.965 ± 0.004, τ = 0.054 ± 0.007, H_0 = 67.4 ± 0.5 km/s/Mpc, and no strong evidence for extensions.
Reheating temperature and equation-of-state parameter assumptions in Weyl-invariant Einstein-Cartan gravity models significantly alter predicted inflationary observables.
Differences in inflationary energy scales between Einstein and Jordan frames produce distinct reheating e-folding numbers and temperatures, leading to contrasting thermal histories with potential observational signatures.
Multi-phase non-minimal inflation in metric and Palatini gravity predicts ns between 0.93 and 0.98, r up to 0.03 in metric but below 10^{-5} in Palatini, with non-thermal DM and leptogenesis viable for couplings in the 10^{-7} to 10^{-3} range.
Gravity-mediated production of scalar and vector dark radiation yields Planck 2018 constraints on reheating temperature T_RH and background equation of state w_Φ, with comparisons to right-handed neutrinos, ALPs, and a generic spin-2 mediator.
A review summarizing the Hubble constant tension and proposed solutions from new physics that restore agreement between Planck CMB data and local H0 measurements within 1-2 sigma.
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Jordan Frame in Supergravity and Cosmology
The paper introduces new exponential and polynomial supergravity ξ-attractor models in the Jordan frame with non-minimal coupling and shows that Palatini gravity with independent affine connection has no supergravity embedding.
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Quasi-pole inflation in metric-affine gravity
Non-minimal coupling of the inflaton to the Holst invariant in metric-affine gravity induces quasi-pole kinetics that generate an exponential plateau potential and Starobinsky-equivalent predictions regardless of the bare potential.
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Harrison-Zeldovich attractor: From Planck to ACT results
Nonminimal derivative coupling realizes the Harrison-Zeldovich attractor for monomial, hilltop, and α-attractor E-models, pulling them to the scale-invariant spectrum suggested by ACT data.
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Inflaton Accretion onto Primordial Black Holes During Reheating
Inflaton accretion during reheating drives non-linear PBH mass growth that extends lifetimes and amplifies emitted SGWB by multiple orders of magnitude.
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New Exponential and Polynomial $\xi$-attractors
New ξ-attractors with non-minimal coupling and non-canonical kinetics yield Einstein-frame exponential and polynomial potentials whose ns spans 1-2/N to 1-1/N and r can reach zero as ξ grows, fitting Planck, BICEP/Keck, ACT, SPT, and DESI data, plus a supergravity realization.
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High Frequency Spectrum of Primordial Gravitational Waves
High-frequency primordial gravitational waves extend to higher frequencies due to post-inflation inflaton dynamics, and their detailed spectrum shape can distinguish inflation models.
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Testing $\alpha$-attractor P-model of inflation by Cosmic Microwave Background radiation
Polynomial α-attractor P-models of inflation accommodate Planck and Planck+ACT CMB data for ranges of reheating temperatures when decays and fragmentation are included.
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Planck 2018 results. VI. Cosmological parameters
Final Planck CMB data confirms the flat 6-parameter ΛCDM model with Ω_c h² = 0.120 ± 0.001, Ω_b h² = 0.0224 ± 0.0001, n_s = 0.965 ± 0.004, τ = 0.054 ± 0.007, H_0 = 67.4 ± 0.5 km/s/Mpc, and no strong evidence for extensions.
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Reheating in geometric Weyl-invariant Einstein-Cartan gravity
Reheating temperature and equation-of-state parameter assumptions in Weyl-invariant Einstein-Cartan gravity models significantly alter predicted inflationary observables.
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Einstein or Jordan: seeking answers from the reheating constraints
Differences in inflationary energy scales between Einstein and Jordan frames produce distinct reheating e-folding numbers and temperatures, leading to contrasting thermal histories with potential observational signatures.
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Induced Multi-phase Inflation with Reheating: Leptogenesis and Dark Matter Production in Metric versus Palatini
Multi-phase non-minimal inflation in metric and Palatini gravity predicts ns between 0.93 and 0.98, r up to 0.03 in metric but below 10^{-5} in Palatini, with non-thermal DM and leptogenesis viable for couplings in the 10^{-7} to 10^{-3} range.
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CMB signatures of gravity-mediated dark radiation in $\mathbf{\Delta N_{\rm eff}}$
Gravity-mediated production of scalar and vector dark radiation yields Planck 2018 constraints on reheating temperature T_RH and background equation of state w_Φ, with comparisons to right-handed neutrinos, ALPs, and a generic spin-2 mediator.
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In the Realm of the Hubble tension $-$ a Review of Solutions
A review summarizing the Hubble constant tension and proposed solutions from new physics that restore agreement between Planck CMB data and local H0 measurements within 1-2 sigma.
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