A unified model of dark energy and inflation from the Markov-Mukhanov action

TL;DR

This work proposes a unified mechanism for inflation and dark energy via the Markov-Mukhanov modification, where a scalar matter-gravity coupling $\chi(\varepsilon)$ induces running $G(\varepsilon)$ and $\Lambda(\varepsilon)$. Two explicit forms, a linear truncation $\chi(\varepsilon)=1-\varepsilon/\varepsilon_c$ and an all-orders resummation $\chi(\varepsilon)=1/(1+\varepsilon/\varepsilon_c)$, yield distinct early-universe behaviors: Model I features a bouncing cosmology, while Model II begins in an asymptotically de Sitter phase that can generate inflation. In Model II, viable inflation requires a near-deser $w_{\rm DE} \approx -0.99$ and a small effective sound speed $c_e$, and the paper derives the perturbation spectra, showing consistency with Planck, BK18, ACT, and DESI constraints for appropriate parameter choices. The results imply that late-time dynamical dark energy, as hinted by DESI, can be naturally connected to early-universe dynamics through UV corrections encoded in the MM coupling, potentially removing the need for a separate inflaton field. This framework offers a testable link between high-energy gravity corrections and observable cosmology.

Abstract

We propose a unified model of dark energy and inflation through the Markov-Mukhanov modification of the Einstein-Hilbert action, where the matter sector is coupled to gravity via a scalar coupling function depending only on the energy density of the matter content. We assume that the coupling function encodes the UV corrections to the standard model of cosmology and we determine the form of the coupling that allows for the dark energy component to be dynamical and act as the inflaton field in the early universe. Interestingly we show that our model, in order to account for inflation, prefers a dark energy equation of state with $w$ close but not equal to $-1$ in agreement with the latest DESI data.

Figures (7)

• Figure 1: Evolution of the scale factor $a$ for a matter dominated cosmology for model I (left panel) and model II (right panel). The left panel shows a bouncing behavior consistent with similar models obtained in LQC. The right panel shows an asymptotically-de Sitter initial state. In both the plots, we have assumed a purely matter dominated universe today. In both plots, the solid line represents a singular dust FRW universe, while the dashed and dotted lines correspond to different values of $\varepsilon_0/\varepsilon_c$ with values of $\varepsilon_c$ chosen for illustrative purposes.
• Figure 2: Behavior of the running Newton's constant $G(\varepsilon)$ as a function of the scale factor for model I (left panel) and model II (right panel). In both the plots, we have assumed a universe with matter, radiation and a dark energy component with $w_{\rm DE}=-0.99$ and all the density parameters are set from the fiducial values obtained in Planck:2018jri. The solid, dashed and dotted lines in both the plots correspond to different values of $\varepsilon_0/\varepsilon_c$ with values of $\varepsilon_c$ chosen for illustrative purposes.
• Figure 3: Behavior of the running cosmological constant $\Lambda(\varepsilon)$ as a function of the scale factor for model I (left panel) and model II (right panel). In both the panels, we have assumed a universe with matter, radiation and a dark energy component with $w_{\rm DE}=-0.99$ and all the density parameters $\Omega_{i0}$ are set from the fiducial values obtained in Planck:2018jri. The solid, dashed and dotted lines in both the plots correspond to different values of $\varepsilon_0/\varepsilon_c$ with values of $\varepsilon_c$ chosen for illustrative purposes.
• Figure 4: The comoving Hubble radius as a function of the scale factor for the model with only first order correction to the coupling function (left panel) and the model with infinite orders of correction to the coupling function (right panel). In both the plots, we have assumed a universe with matter, radiation and a dark energy component with $w_{\rm DE}=-0.99$ and all the density parameters are set from the fiducial values obtained in Planck:2018jri. The solid line in both the plots correspond to the $\Lambda$CDM model and the dotted and dashed lines correspond to the respective models for different values of $\varepsilon_0/\varepsilon_c$.
• Figure 5: The slow-roll parameters $\epsilon_1$ (left panel) and $\epsilon_2$ (right panel) as functions of $\varepsilon/\varepsilon_c$ for different matter contents of the universe. Notice that while the first slow-roll parameter tends to zero for $\varepsilon$ large, the second slow roll parameter tends to a constant $\epsilon_2\rightarrow 3(1+w)$ and thus remains small only for suitable values of the equation of state parameter $w$.