Schrödinger-type $f(Q,T)$ gravity-nonmetricity driven cosmological evolution from inflation to the late Universe

TL;DR

This work introduces a Schrödinger-type $f(Q,T)$ gravity with a vectorial non-metricity that preserves vector lengths and enforces a flat background via a Lagrange multiplier. The authors derive the action, field equations, and a generalized set of Friedmann equations for a flat FLRW Universe, revealing additional geometric contributions that act as an effective dark energy. They explore geometry-driven warm inflation, including exact solutions with constant non-metricity and dynamical Lagrange multiplier, showing radiation production and a transition from inflation to deceleration. They then confront a simple linear $f(Q,T)$ model with Cosmic Chronometers, Pantheon+ SNe Ia, and BAO data using nested sampling, finding good agreement with late-time data and a competitive fit to ΛCDM, along with distinctive evolution of the nonmetricity and Lagrange multiplier. Overall, the Schrödinger-type $f(Q,T)$ framework provides a viable geometric extension of gravity capable of describing both early and late cosmological evolution, and it offers a novel mechanism for radiation production tied to spacetime geometry.

Abstract

We consider an $f(Q, T)$ gravity theory with a Schrödinger type vectorial non-metricity. In the presence of such a non-metricity, the length of vectors is preserved under autoparallel transport. We obtain the field equations assuming a vanishing total scalar curvature, implemented by a Lagrange multiplier, and investigate their cosmological implications. To do this, we derive the generalized Friedmann equations which now have terms involving the non-metricity and the Lagrange multiplier. Then, we consider two distinct cosmological applications of the model. First of all, by adopting distinct forms of these two basic variables and investigate the possibility of the existence of warm inflationary scenarios within the framework of these models. In particular, we consider the case that the non-metricity is described by a constant vector, and we show that with this assumption we recover standard general relativity. The scenario in which the Lagrange multiplier is a constant is also investigated, and we show that radiation can be created during the very early phases of expansion. The amount of radiation peaks at a certain time after which, there is a transition from an accelerating inflationary phase to a decelerating one. Moreover, we perform a detailed comparison of the predictions of the considered Schrödinger type cosmology with a set of observational data for the Hubble function, including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations, using a Markov Chain Monte Carlo (MCMC) analysis, by adopting a simple linear form for the Lagrange density. The model predictions are also compared with the results of the $Λ$CDM standard paradigm. Our results indicate that the Schrödinger $f(Q,T)$ type theory can give a good description of the observational data for both the very early and the late Universe.

Figures (10)

• Figure 1: Illustration of several flat geometries with nonmetricity.
• Figure 2: Variation of the matter energy density during the warm inflationary phase of evolution of the Universe in the Schrödinger type $f(Q,T)$ theory, for different values of the constant non-metricity vector $\Pi_0$: $\Pi_0 =0.05$ (solid curve), $\Pi_0 =0.0.0505$ (short dashed curve), $\Pi_0 =0.0507$ (dashed curve), $\Pi_0 =0.0509$ (long dashed curve), and $\Pi_0 =0.051$ (ultra-long dashed curve). The numerical values of the free parameters of the constant non-metricity model have been fixed to $C_1=2$, $M=0.9$, and $\alpha =-0.9$, respectively.
• Figure 3: Variation of the radiation energy density during the warm inflationary phase of evolution of the Universe in the Schrödinger type $f(Q,T)$ theory, for various values of $\alpha$: $\alpha =6$ (solid curve), $\alpha =7$ (short dashed curve), $\alpha =8$ (dashed curve), $\alpha =9$ (long dashed curve), and $\alpha =10$ (ultra-long dashed curve). The numerical values of $M$ has been fixed to $M^2=1$. The initial value of the time variable was taken as $\tau _0=10^{-10}$. The initial conditions used to numerically integrate the system of evolution equations are $h\left(\tau_0\right)=0.11$, $r\left(\tau_0\right)=10^{-10}$, $\Pi \left(\tau_0\right)=0.01$, and $\Lambda \left(\tau_0\right)=150$, respectively.
• Figure 4: Variation of the Hubble function during the warm inflationary phase of evolution of the Universe in the Schrödinger type $f(Q,T)$ theory, for various values of $\alpha$: $\alpha =6$ (solid curve), $\alpha =7$ (short dashed curve), $\alpha =8$ (dashed curve), $\alpha =9$ (long dashed curve), and $\alpha =10$ (ultra-long dashed curve). The numerical values of $M$ has been fixed to $M^2=1$. The initial value of the dimensionless time variable $\tau$ was taken as $\tau _0=10^{-10}$. The initial conditions used to numerically integrate the system of evolution equations are $h\left(\tau_0\right)=0.11$, $r\left(\tau_0\right)=10^{-10}$, $\Pi \left(\tau_0\right)=0.01$, and $\Lambda \left(\tau_0\right)=150$, respectively.
• Figure 5: Time variations Schrödingerödinger vector (left panel) and of the Lagrange multiplier $\lambda$ (right panel) during the warm inflationary phase of evolution of the Universe in the Schrödinger type $f(Q,T)$ gravity, for various values of $\alpha$: $\alpha =6$ (solid curve), $\alpha =7$ (short dashed curve), $\alpha =8$ (dashed curve), $\alpha =9$ (long dashed curve), and $\alpha =10$ (ultra-long dashed curve). The numerical values of $M$ has been fixed to $M^2=1$. The initial value of the dimensionless time variable $\tau$ was taken as $\tau _0=10^{-10}$. The initial conditions used to numerically integrate the system of evolution equations are $h\left(\tau_0\right)=0.11$, $r\left(\tau_0\right)=10^{-10}$, $\Pi \left(\tau_0\right)=0.01$, and $\Lambda \left(\tau_0\right)=150$, respectively.