Study uses concepts from thermodynamics to describe the expansion of the Universe

The idea of expansion of the Universe It's almost a century old. The proposition that distant galaxies are moving away from Earth and that their speed of separation increases with distance was theorized by the Belgian Georges Lemaître (1894-1966) in 1927 and confirmed observationally by the North American Edwin Hubble (1889-1953) two years later. This confirmation was provided by the redshift (redshift) of the spectrum of electromagnetic radiation received from these distant objects.

In 1998, a surprising new ingredient was added to the model. A set of observations of very distant supernova stars, carried out by the Supernova Cosmology Project and by High-Z Supernova Search Teamshowed that the expansion of the Universe was accelerating – and not being slowed down by gravitational effect as supposed.

This discovery led to the concept of dark energy which is assumed to contribute more than 68% of the total energy of the current observable Universe, while dark matter and ordinary matter contribute approximately 26% and 5%.

“Measures of redshift point to an accelerated adiabatic expansion [isto é, sem troca de calor] and anisotropic [que não é a mesma em todas as direções]”, says Mariano de Souza, professor in the Department of Physics at the Institute of Geosciences and Exact Sciences at the Universidade Estadual Paulista (Unesp), Rio Claro campus. And he continues: “Fundamental concepts of thermodynamics allow us to infer that every adiabatic expansion is accompanied by cooling, in the barocaloric effect [capaz de gerar calor quando submetido a pressão] which is quantified by the so-called Grüneisen ratio.”

Some information is in order here. In 1908, the German physicist Eduard August Grüneisen (1877-1949) proposed a mathematical expression for the so-called effective Grüneisen parameter, Γ_effwhich relates three physical properties of a material: the coefficient of thermal expansion, the specific heat and the isothermal compressibility.

Almost a century later, in 2003, Lijun Zhu and collaborators demonstrated that the singular part of Γ_effcall “Grüneisen ratio ”, defined as the ratio between the coefficient of thermal expansion and specific heat, increases significantly in the vicinity of a quantum critical point due to the accumulation of entropy. In 2010, Mariano de Souza and collaborators demonstrated that the same occurs for a critical point at finite temperature.

In a recent article, published in the journal Results in Physics, Unesp researchers led by Souza used the Grüneisen parameter to describe intricate aspects related to the expansion of the Universe. The work is one of the results of doctoral research by Lucas Squillante, the first author, currently a postdoctoral student under the supervision of Souza.

“The dynamics associated with the expansion of the Universe are generally described by the model of a perfect fluid, whose equation of state is given by ω = p/ρ, where ω [ômega] is the so-called parameter of the state equation, p [pê] the pressure and ρ [rô] the energy density. Although widely used, the physical meaning of ω had not yet been properly discussed. In other words, ω was treated only as a constant for each era of the Universe. One of the important results of our work is the identification of ω with the effective Grüneisen parameter, through the Mie-Grüneisen equation of state”, explains Souza.

The researchers demonstrated, using the Grüneisen parameter, that the continuous cooling of the Universe is associated with a barocaloric effect, that is, that relates pressure and temperature . This effect, in turn, occurs due to the adiabatic expansion of the Universe. From this perspective, they proposed that, in the era dominated by dark energy, in which we currently find ourselves, the Grüneisen parameter depends on time.

One of the interesting aspects of this work is that it uses concepts of thermodynamics and solid state physics as stress (voltage) and strain (deformation), to describe the anisotropic expansion of the Universe.

“We demonstrated that the Grüneisen parameter is naturally included in the stress tensor. stress energy-momentum present in Einstein's celebrated field equations – which provides a new way of investigating anisotropic effects associated with the expansion of the Universe. These do not exclude the scenario of a possible Big Rip”, says Souza.

The hypothesis of Big Rip (Great Rupture) was first performed in 2003, in article published in Physical Review Letters. She says that if the amount of dark energy is enough to accelerate the expansion of the Universe beyond a critical speed, it could cause a tear in the “fabric” of space-time.

“Still from the perspective of the Grüneisen parameter, we conjecture that the change from a regime of slowed expansion [na era dominada pela radiação e pela matéria] for an accelerated expansion regime [na era dominada pela energia escura] resembles a thermodynamic phase transition. This is because we demonstrated that Γ_eff changes sign when the expansion of the universe changes from slowed to accelerated. Such a change in sign resembles the typical signature of phase transitions in condensed matter physics”, adds Souza.

As is known, dark energy was associated with the cosmological constant Λ [lambda]. First postulated and then rejected by Einstein, the cosmological constant was rehabilitated when it was discovered that the expansion of the Universe was accelerating rather than slowing down.

The hegemonic model, called Λ-CMD (Lambda-Cold Dark Matter), gives the cosmological constant a fixed value. That is, it assumes that the density of dark energy remains constant as the Universe expands. But there are other models that assume that the density of dark energy, and consequently Λ, varies over time.

“Assigning a fixed value to lambda is equivalent to also assigning a fixed value to omega. But recognizing ω as the effective Grüneisen parameter allows us to infer a temporal dependence of ω as the Universe expands in the era dominated by dark energy. And this directly implies a temporal dependence on Λ or the universal constant of gravitation”, highlights Souza. The study, as can be seen, opens a new way of interpreting the expansion of the Universe in the light of thermodynamics and concepts of condensed matter physics and may have important consequences.

In addition to Souza and Squillante, researchers participated in the study Antonio Seridonio (Unesp of Ilha Solteira), Roberto Lagos-Monaco (Unesp of Rio Claro), Gabriel Gomes (Institute of Astronomy, Geophysics and Atmospheric Sciences of the University of São Paulo, IAG-USP), Guilherme Nogueira (Unesp de Rio Claro) and doctoral student Isys Mello, Souza's advisor.

The work received support from FAPESP through two projects (11/22050-4 It is 18/09413-0 ).

The article Exploring the expansion of the universe using the Grüneisen parameter can be accessed at: www.sciencedirect.com/science/article/pii/S2211379724000263?via%3Dihub .