arXiv subjects

William H. Kinney

Publications and source records attributed to William H. Kinney.

At least 19 recordsLinked to original sources

arXiv2026

An Inverse Lyth Bound for Non-Attractor Inflation

I present a novel physics result generated entirely autonomously by ChatGPT 5.6 Sol. The Lyth bound relates an observable primordial tensor amplitude to a lower limit on the field excursion during single-field slow-roll inflation. We show that non-attractor evolution obeys a complementary upper bound. For a canonically normalized scalar field, the nonconstant superhorizon curvature mode is anti-damped whenever the second Hubble-flow parameter satisfies $\epsilon_2\equiv d\ln\epsilon/dN<-3$. The same condition requires the inflaton kinetic energy to decrease sufficiently rapidly that the field-space distance traversed during a non-attractor interval obeys $\Delta\phi_{\rm NA} / M_{\text{P}} < \left(2\sqrt{2\epsilon_{\rm in}}/3\right) \left(1-e^{-3\Delta N/2}\right) < \left(2\sqrt{2\epsilon_{\rm in}}/3\right)$.The result is independent of the potential and does not require the slow-roll approximation. If $\epsilon_2=-p<-3$ is constant, the stronger bound $\Delta\phi/M_{\text{P}}<2\sqrt{2\epsilon_{\rm in}}/p$ is saturated asymptotically. In ultra-slow-roll inflation, $p=6$, giving $\Delta\phi<\sqrt{2\epsilon_{\rm in}}M_{\text{P}}/3$. We derive an exact relation between field excursion and amplification of the velocity of the nonconstant curvature mode, and give the corresponding scalar-power relation in the quasi-de Sitter limit. In contrast with the usual Lyth relation, arbitrarily large non-attractor amplification approaches a finite field distance. This provides a model-independent field-range constraint on canonical single-field mechanisms for amplifying primordial fluctuations.

astro-ph.CO↗

arXiv2026

The BGV Theorem and the Null Convergence Condition

We examine the relationship between the Null Convergence Condition (NCC) and the Borde-Guth-Vilenkin (BGV) Theorem. We first show that, for an expanding spacetime foliated orthogonally to a timelike geodesic congruence with vanishing shear and vorticity, the BGV Theorem follows when the NCC holds and the spatial curvature is non-positive, ${}^3\mathcal{R} \leq 0$. The situation becomes more complex in the presence of shear, or non-geodesic threading of the spacetime. In these cases, the local expansion that enters the BGV construction depends not only on the local scalar expansion, but acquires terms given by the contraction of the shear and acceleration with locally defined spatial unit vectors. In the general case, null convergence and non-positive curvature are no longer sufficient to guarantee that the BGV Theorem holds. We discuss the result in the context of eternal inflation in the presence of comoving curvature perturbations and state a more general version of the BGV condition relevant to asymptotically past-de Sitter eternal inflation.

gr-qc↗

arXiv2026

Phase Transitions and Gravitational Waves

We present a Fisher matrix forecast for the spectral parameter reconstruction of a stochastic gravitational wave background generated by a first-order phase transition in the early universe. We use the LISA and DECIGO instruments for reference and model the source spectrum with a double-broken-power-law template, parameterized by the peak amplitude $\Omega_p$, peak frequency $f_p$, break ratio $r_b$, and intermediate slope $b$. For each detector, we construct a fixed fiducial benchmark with the peak placed in the corresponding sensitivity band, using $f_p=3.0\times10^{-3} \ {\rm Hz}$ for LISA and $f_p=1.0\ {\rm Hz}$ for DECIGO. The LISA baseline includes an unresolved galactic compact-binary foreground, while for DECIGO we compare foreground cases using a full compact binary, a projected post-subtraction compact-binary residual, and an instrument noise only foreground. We find that both detectors constrain the peak parameters $\ln\Omega_p$ and $\ln f_p$ more robustly than the detailed shape parameters $r_b$ and $b$. For the chosen DECIGO benchmark, the projected residual foreground produces negligible parameter degradation relative to the instrument noise only case, while the full foreground lowers the signal-to-noise ratio from $\rho=10$ to $\rho\simeq6.06$ and increases the marginalized uncertainty on $b$ by about $51\%$. These results emphasize that stochastic-background forecasts should distinguish detectability from spectral identifiability.

gr-qc↗

arXiv2026

Geodesic Completeness in General Cosmological Scenarios

The well-known Borde-Guth-Vilenkin Theorem shows that inflationary spacetimes are generically geodesically past-incomplete, necessitating the existence of a pre-inflationary boundary of some sort, possibly singular. I discuss the generalization of the BGV theorem to spacetimes beyond inflation, including inhomogeneous and cyclic models. As an example, I show that the cyclic model proposed by Ijjas and Steinhardt is geodesically incomplete.

gr-qc↗

arXiv2024

A bound on thermal y-distortion of the cosmic neutrino background

We consider the possibility that the cosmic neutrino background might have a nonthermal spectrum, and investigate its effect on cosmological parameters relative to standard $Λ$-Cold Dark Matter ($Λ$CDM) cosmology. As a specific model, we consider a thermal $y$-distortion, which alters the distribution function of the neutrino background by depleting the population of low-energy neutrinos and enhancing the high-energy tail. We constrain the thermal $y$-parameter of the cosmic neutrino background using Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillation (BAO) measurements, and place a $95\%$-confidence upper bound of $y \leq 0.043$. The $y$-parameter increases the number of effective relativistic degrees of freedom, reducing the sound horizon radius and increasing the best-fit value for the Hubble constant $H_0$. We obtain an upper bound on the Hubble constant of $H_0 = 71.12\ \mathrm{km/s/Mpc}$ at $95\%$ confidence, substantially reducing the tension between CMB/BAO constraints and direct measurement of the expansion rate from Type-Ia supernovae. Including a spectral distortion also allows for a higher value of the spectral index of scalar fluctuations, with a best-fit of $n_{\mathrm{S}} = 0.9720 \pm 0.0063$, and a $95\%$-confidence upper bound of $n_{\mathrm{S}} \leq 0.9842$.

astro-ph.CO↗

arXiv2024

The Borde-Guth-Vilenkin Theorem in extended de Sitter spaces

The Borde-Guth-Vilenkin (BGV) theorem states that any spacetime with net positive expansion must be geodesically incomplete. We derive a new version of the theorem using the fluid flow formalism of General Relativity. The theorem is purely kinematic, depending on the local expansion properties of geodesics, and makes no assumptions about energy conditions. We discuss the physical interpretation of this result in terms of coordinate patches on de Sitter space, and apply the theorem to Penrose's model of Conformal Cyclic Cosmology. We argue that the Conformal Cyclic extension of an asymptotically de Sitter universe is geodesically incomplete.

gr-qc↗

arXiv2022

Simple single-field inflation models with arbitrarily small tensor/scalar ratio

We construct a family of simple single-field inflation models consistent with Planck / BICEP Keck bounds which have a parametrically small tensor amplitude and no running of the scalar spectral index. The construction consists of a constant-roll hilltop inflaton potential with the end of inflation left as a free parameter induced by higher-order operators which become dominant late in inflation. This construction directly demonstrates that there is no lower bound on the tensor/scalar ratio for simple single-field inflation models.

astro-ph.CO↗

arXiv2022

Cyclic Cosmology and Geodesic Completeness

We consider recently proposed bouncing cosmological models for which the Hubble parameter is periodic in time, but the scale factor grows from one cycle to the next as a mechanism for shedding entropy. Since the scale factor for a flat universe is equivalent to an overall conformal factor, it has been argued that this growth corresponds to a physically irrelevant rescaling, and such bouncing universes can be made perfectly cyclic, extending infinitely into the past and future. We show that any bouncing universe which uses growth of the scale factor to dissipate entropy must necessarily be geodesically past-incomplete, and therefore cannot be truly cyclic in time.

gr-qc↗

arXiv2021

Gravitational Wave Direct Detection does not Constrain the Tensor Spectral Index at CMB Scales

I discuss constraints on the power spectrum of primordial tensor perturbations from a combination of Cosmic Microwave Background (CMB) measurements and the gravitational wave direct detection experiments LIGO/Virgo and DECIGO. There are two main points: (1) Inflation predicts an approximately power-law form for the primordial tensor spectrum, but makes no prediction for its amplitude. Given that neither Planck nor LIGO/Virgo has actually detected primordial tensor modes, it is trivially true that no model-independent constraint on the slope of the tensor power spectrum is possible with current data. (2) CMB and LIGO/Virgo scales differ by more than 19 orders of magnitude, and 16 for DECIGO. I show that a power-law extrapolation from CMB to direct detection frequencies overestimates the amplitude of primordial tensor modes by as much as two orders of magnitude relative to an ensemble of realistic single-field inflation models. Moreover, the primordial tensor amplitude at direct detection scales is mostly uncorrelated with the tensor spectral index at CMB scales, and any constraint is strongly dependent on the specific form of the inflationary potential.

astro-ph.CO↗

arXiv2021

Natural Inflation After Planck 2018

We calculate high-precision constraints on Natural Inflation relative to current observational constraints from Planck 2018 + BICEP/Keck(BK15) Polarization + BAO on $r$ and $n_S$, including post-inflationary history of the universe. We find that, for conventional post-inflationary dynamics, Natural Inflation with a cosine potential is disfavored at greater than 95\% confidence out by current data. If we assume protracted reheating characterized by $\overline{w}>1/3,$ Natural Inflation can be brought into agreement with current observational constraints. However, bringing unmodified Natural Inflation into the 68\% confidence region requires values of $T_{\mathrm{re}}$ below the scale of electroweak symmetry breaking. The addition of a SHOES prior on the Hubble Constant $H_0$ only worsens the fit.

astro-ph.CO↗

arXiv2021

The Swampland Conjecture Bound Conjecture

I conjecture an upper bound on the number of possible swampland conjectures by comparing the entropy required by the conjectures themselves to the Beckenstein-Hawking entropy of the cosmological horizon. Assuming of order 100 kilobits of entropy per conjecture, this places an upper bound of order $10^{117}$ on the number of conjectures. I estimate the rate of production of swampland conjectures by the number of papers listed on INSPIRE with the word "swampland" in the title or abstract, which has been showing approximately exponential growth since 2014. At the current rate of growth, the entropy bound on the number of swampland conjectures can be projected to be saturated on a timescale of order $10^{-8} H_0^{-1}$. I compare the upper bound from the Swampland Conjecture Bound Conjecture (SCBC) to the estimated number of vacua in the string landscape. Employing the duality suggested by AdS/CFT between the quantum complexity of a holographic state and the volume of a Wheeler-Dewitt spacetime patch, I place a conservative lower bound of order $\mathcal{N}_H > 10^{263}$ on the number of Hubble volumes in the multiverse which must be driven to heat death to fully explore the string landscape via conjectural methods.

hep-th↗

arXiv2020

The Trans-Planckian problem in Tachyacoustic Cosmology

We study Tachyacoustic models of cosmology, for which a scale-invariant perturbation spectrum is generated via superluminal sound speed instead of accelerated expansion, as in the case of inflation. We derive two bounds on the size of acoustic horizon which constrain the duration of tachyacoustic evolution, and therefore generation of primordial perturbations. We show that existing models cannot solve the horizon problem without violating the condition that all physical scales -- such as the Hubble parameter, the pressure, and the length scale at which quantum modes freeze out and become classical -- be sub-Planckian.

gr-qc↗

arXiv2020

Trans-Planckian Censorship and $k$-inflation

We propose a more general version of the Trans-Planckian Censorship Conjecture (TCC) which can apply to models of inflation with varying speed of sound. We find that inflation models with $c_S < 1$ are in general more strongly constrained by censorship of trans-Planckian modes than canonical inflation models, with the upper bound on the tensor/scalar ratio reduced by as much as three orders of magnitude for sound speeds consistent with bounds from data. In particular, models which satisfy the TCC, and therefore the de Sitter Swampland Conjecture, can still violate the more general condition for non-classicality of trans-Planckian modes. As a concrete example, we apply the constraint to Dirac-Born-Infeld inflation models motivated by string theory.

gr-qc↗

arXiv2019

Consistency of Tachyacoustic Cosmology with de Sitter Swampland Conjectures

Recent studies show that there is tension between the de Sitter swampland conjectures proposed by Obeid, et al. and inflationary cosmology. In this paper, we consider an alternative to inflation, `tachyacoustic' cosmology, in light of swampland conjectures. In tachyacoustic models, primordial perturbations are generated by a period of superluminal sound speed instead of accelerating expansion. We show that realizations of tachyacoustic Lagrangians can be consistent with the de Sitter swampland conjectures, and therefore can in principle be consistent with a UV-complete theory. We derive a general condition for models with $c_S > 1$ to be consistent with swampland conjectures.

astro-ph.CO↗

arXiv2019

Dynamical Analysis of Attractor Behavior in Constant Roll Inflation

There has been considerable recent interest in a new class of non-slow roll inflationary solutions known as \textit{constant roll} inflation. Constant roll solutions are a generalization of the ultra-slow roll (USR) solution, where the first Hubble slow roll parameter $ε$ is small, but the second Hubble slow roll parameter $η$ is not. While it is known that the USR solutions represent dynamical transients, there has been some disagreement in literature about whether or not large-$η$ constant roll solutions are attractors or are also a class of transient solutions. In this paper we show that the large-$η$ constant roll solutions do in fact represent transient solutions by performing stability analysis on the exact analytic (large-$η$) constant roll solutions.

astro-ph.CO↗

arXiv2019

The zoo plot meets the swampland: mutual (in)consistency of single-field inflation, string conjectures, and cosmological data

We consider single-field inflation in light of string-motivated "swampland" conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion $Δϕ\lesssim M_{\rm Pl}$, in combination with a sufficiently steep potential, $M_{\rm Pl} V_ϕ/V \gtrsim {\cal O}(1)$. Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the $n_S$-$r$ "zoo plot" of inflationary models, and find that consistency with the Planck satellite and BICEP2/Keck Array requires $M_{\rm Pl} V_ϕ/V \lesssim 0.1$ and $-0.02 \lesssim M_{\rm Pl}^2 V_{ϕϕ}/V < 0$, in strong tension with swampland conjectures. Extension to non-canonical models such as DBI Inflation does not significantly weaken the bound.

astro-ph.CO↗

arXiv2018

Eternal Inflation and the Refined Swampland Conjecture

I apply recently proposed "Swampland" conjectures to eternal inflation in single-scalar field theories. Eternal inflation is a phase of infinite self-reproduction of a quasi-de Sitter universe which has been argued to be a generic consequence of cosmological inflation. The originally proposed de Sitter swampland conjectures were shown by Matsui and Takahashi and by Dimopoulos to be generically incompatible with eternal inflation. However, the more recently proposed "refined" swampland conjecture imposes a slightly weaker criterion on the scalar field potential in inflation, and is consistent with the existence of a tachyonic instability. In this paper, I show that eternal inflation is marginally consistent with the refined de Sitter swampland conjecture. Thus, if the refined conjecture is correct, the existence of a landscape-based "multiverse" in string theory is not incompatible with a self-consistent ultraviolet completion, with significant consequences for model building in string theory.

astro-ph.CO↗

arXiv2018

Large-$η$ Constant-Roll Inflation Is Never An Attractor

Slow roll solutions to inflationary potentials have been widely believed to be the only universal attractor. Over the last few years there has been growing interest in a new class of inflationary models known as Constant-Roll Inflation. Constant roll solutions are a generalization of "ultra-slow roll" dynamics, where the first slow roll parameter is small, but the second slow roll parameter $η$ is larger than unity. In Ultra-slow Roll Inflation, the large-$η$ solution is a dynamical transient, relaxing exponentially to the attractor de Sitter solution. In the constant roll generalization, recent papers have concluded that Constant-Roll Inflation represents a new class of non-slow roll attractor solutions. In this paper we show that these attractor solutions are actually the usual slow roll attractor, disguised by a parameter duality, and that the large-$η$ solutions, as in the case of ultra-slow roll, represent a dynamical transient.

astro-ph.CO↗