[Paper Review] Dark Energy from Quantum Matter

Claudio Dappiaggi, Thomas-Paul Hack+2 more|arXiv (Cornell University)|Jul 28, 2010

Cosmology and Gravitation Theories1 references8 citations

TL;DR

This paper proposes that dark energy and dark matter emerge dynamically from quantum fields in a flat Friedmann-Robertson-Walker spacetime, using a non-perturbative quantization scheme on curved backgrounds. It shows that the trace anomaly and thermal state contributions reproduce the $Λ$CDM model’s late-time acceleration and mimic dark matter, with a fit to supernova data confirming dynamical dark energy and a $T^3$-dependent component matching dark matter scaling.

ABSTRACT

We study the backreaction of free quantum fields on a flat Robertson-Walker spacetime. Apart from renormalization freedom, the vacuum energy receives contributions from both the trace anomaly and the thermal nature of the quantum state. The former represents a dynamical realisation of dark energy, while the latter mimics an effective dark matter component. The semiclassical dynamics yield two classes of asymptotically stable solutions. The first reproduces the concordance model in a suitable regime. The second lacks a classical counterpart, but is in excellent agreement with recent observations.

Motivation & Objective

• To investigate whether dark energy and dark matter can originate from fundamental, non-interacting quantum fields in a cosmological context.
• To determine if the backreaction of quantum fields on spacetime geometry can reproduce the observed accelerated expansion of the Universe.
• To assess whether the thermal nature of quantum states can generate a component with the redshift dependence of dark matter.
• To test the viability of a semiclassical gravity framework with a KMS-like quantum state in cosmology using observational data.

Proposed method

• Uses a non-perturbative quantization scheme for free quantum fields on curved spacetimes, specifically tailored for Robertson-Walker backgrounds.
• Applies the Hadamard condition to define a well-behaved vacuum state and regularize the stress-energy tensor via normal ordering.
• Computes the trace anomaly of the renormalized stress-energy tensor, which includes geometric terms and mass-dependent contributions from scalar, spinor, and vector fields.
• Imposes an approximate KMS condition at an early time $t_0$, assuming a common temperature $T$ for all fields, and expands to lowest order in $T/m$.
• Derives the semiclassical Einstein equations in terms of the Hubble parameter $H$, with the energy density $ ho$ split into geometric and state-dependent parts.
• Fits the resulting Hubble function $H^2(a)$ to type Ia supernova data, using renormalization parameters as free fit parameters to determine $K_1$, $K_2$, $K_3$.

Experimental results

Research questions

• RQ1 Can the trace anomaly of quantum fields on curved spacetime generate a dynamical dark energy component that matches the observed late-time acceleration?
• RQ2 Does the thermal nature of a quantum state in a cosmological setting produce a component with the redshift dependence $a^{-3}$, characteristic of non-relativistic matter?
• RQ3 Can a quantum field theory framework on curved spacetime reproduce the $Λ$CDM model’s observational features without introducing a cosmological constant?
• RQ4 Is the effective dark matter component arising from quantum state thermal properties consistent with astrophysical observations of dark matter haloes?

Key findings

• The model yields two asymptotically stable solutions to the semiclassical Einstein equations, both fitting supernova data as well as the $Λ$CDM model.
• The $K_1$ term in the Hubble function $H^2(a) ≈ K_1 + K_2 a^{-3} + K_3 a^{-6}$ arises from the trace anomaly and acts as a dynamical dark energy component.
• The $K_2 a^{-3}$ term, originating from the thermal state's contribution to the zero-point energy, scales like matter and mimics dark matter, with a $T^3$ dependence instead of $a^{-3}$ from particle density.
• The fit to supernova data implies $K_3 ≈ 10^{-3} H_0^2$, confirming the model’s ability to reproduce the concordance model in the recent past.
• Assuming a single mass scale $m$, the temperature $T$ must satisfy $m = 10\,\text{eV} \left(\frac{1\,\text{K}}{T}\right)^3$, linking quantum parameters to cosmological scales.
• The thermal contribution to the vacuum energy density on a static spacetime yields a profile $\propto |g_{00}|^{-3/2}$, matching the observed $r^{-3}$ decay in dwarf spheroidal galaxies.