Inflation from entropy

TL;DR

This work develops a gravity-from-entropy framework in which gravity is governed by the quantum relative entropy between the spacetime metric and a geometry–matter induced metric, leading to modified Friedmann equations. In vacuum these equations admit inflationary solutions without invoking an inflaton or exotic matter, featuring two main x = $GH^2$ branches and a phantom-like regime; slow-roll dynamics can reproduce CMB observables under standard mappings. The high-entropy inflationary branch with $0.12 \lesssim x \lesssim 1/6$ yields tensor-to-scalar ratios $r$ in the range $\sim 10^{-4}$–$10^{-2}$ and scalar spectral indices $n_s \approx 0.962$–$0.964$, aligning with Planck constraints, while the phantom-like window offers alternative early-Universe phenomenology. Entropy-based interpretation suggests a greater geometric degrees of freedom in inflationary solutions and motivates further perturbation analyses and exploration of bounce or cyclic cosmologies within this entropic gravity framework.

Abstract

We investigate cosmological solutions for the modified gravity theory obtained from quantum relative entropy between the metric of spacetime and the metric induced by the geometry and matter fields. The vacuum equations admit inflationary solutions, hinting at an entropic origin for inflation. Equations also admit a regime of phantom like behavior. Assuming that the relation between slow roll parameters and CMB observables holds for entropic gravity, the theory predicts a viable spectrum.

Figures (6)

• Figure 1: $\epsilon$ and $\eta$ as a function of number of e-folds for $x=10^{-2}$. Solutions represent a slow roll scenario where $\abs{\eta} \ll1$ and $\epsilon \ll1$
• Figure 2: Evolution of the Hubble (top) and slowroll (bottom) parameters with number of e-folds N starting from for initial conditions $H(0)=10^{-9}$ and $H'(0)=3/16 \times 10^{-9}$
• Figure 3: $\epsilon$ and $\eta$ as a function $x$ after 50 e folds of inflation. Solutions are slow rolling with $\abs{\eta} \ll1$ and $0<\epsilon \ll1$ for $0<x\mathrel{\hbox{$\sim$} \hbox{$<$}}0.08$ and $0.12 \mathrel{\hbox{$\sim$} \hbox{$<$}} x <1/6$.
• Figure 4: Tensor to scalar ratio vs spectral index plot for $0.12 \mathrel{\hbox{$\sim$} \hbox{$<$}} x < 1/6$ after 55 e-folds of inflation.
• Figure 5: Slow roll parameter $\epsilon$ as a function of number of e-folds for $x=0.1$. The slow roll parameter is small and negative but increasing over time.