Can Scalaron Be Dark Matter? (Quantum Physics / Maths / Cosmology)

Shtanov showed that scalaron can play a role of dark matter if its mass is about m = 4.4 × 10¯3 eV.

Several researchers explored the possibility that dark matter in our universe can be explained in the context of f(R) gravity models. In these models, dark matter is associated with the scalaron field that arises when proceeding from the Jordan frame to the Einstein frame by a conformal transformation of the metric. An appealing feature of this approach is that a dark-matter candidate arises here purely from the gravitational sector, without introducing new fundamental fields.

In most papers on the subject, the usual matter is treated macroscopically and is characterised by averaged energy density and pressure in the Jordan frame. The scalaron mass then depends on the matter density, varying in time and over different astrophysical objects. Now, Yuri Shtanov in his recent paper, proposed to describe the usual matter by the fundamental Standard-Model action in the Jordan frame, and take into account the conformal properties of this action to proceed to the Einstein frame.

“One thus obtains a model with the Einstein gravity and with non-trivial interaction between the scalaron and the Higgs field, which can be taken as the starting point.”

— told Shtanov, author of the study

Based on such a model, he proposed a new cosmological scenario with the scalaron playing the role of dark matter in the f(R) gravity. Starting from the Standard Model action in the Jordan frame, he proceeded to the Einstein frame and obtained theory given below,

In this equation, they observed the appearance of non-renormalisable interactions of the scalaron ϕ with the higgs field © Shtanov et al.

in which the scalaron interacts non-trivially with the Higgs field. The scalaron is then assumed to reside initially in the minimum of its effective potential while the electroweak symmetry was unbroken. The subsequent evolution of the Higgs field during the electroweak crossover triggers the evolution of the scalaron. It starts oscillating with decreasing amplitude around its stationary point and, eventually, plays the role of dark matter if its mass is about m = 4.4 × 10¯3 eV.

“In our scenario, the scalaron always remains in the region of values φ ≪ M, so that the issues of non-renormalisability and quantum corrections to the scalaron effective potential are of no crucial importance.”

— told Shtanov, author of the study

For the same reason, he suggested that the specific form of the f(R) theory in equation,

where, M is a conveniently normalised Planck mass, M = √(3/16πG) ≈ 3 × 1018 GeV, and Λ ≈ (3 × 10¯33 eV)2 is the cosmological constant in the natural units ¯h = c = 1.

is not crucial; all that is required is that the resulting scalaron potential has a minimum with potential corresponding to the current cosmological constant and with mass “m” of the indicated order of 10¯3 eV.

In addition, he mentioned that the fixed stationary initial condition of the scalaron field distinguishes the described scenario. If, however, one assumes that the scalaron is excited prior to the electroweak transition, then its initial energy density may be larger than it is in the described scenario. In the same ratio will be larger its current energy density, and the mass “m” required to ensure the correct amount of dark matter will also be larger.

Moreover, it has been shown that the quantum scale anomalies arising when proceeding from the Jordan to Einstein frame generate couplings between the scalaron and gauge fields of the form:

where, α = g2/4π is the gauge coupling constant. They may lead to scalaron decays into a pair of photons, with lifetime τ ∼ M22m3 ∼ 1036(eV/m)3 yr, far exceeding the age of the universe (1.4 × 1010 yr) for their values of the mass “m”. The scalaron can then be regarded practically as a stable particle.

“Since the scalaron was used here to describe dark matter, inflation might be based on the Higgs coupling to the scalar curvature. Such a combined model remains to be elaborated.”

— told Shtanov, author of the study

Finally, he mentioned that mass scale of the order present in their result,

also arises in the context of dark energy and neutrino oscillations. Thus, the dark-energy density can be expressed as

while, for the differences of squared masses in solar-neutrino oscillations, they have,

This work was supported by the National Research Foundation of Ukraine under Project No. 2020.02/0073

For more:

Yuri Shtanov, “Light scalaron as dark matter”, Arxiv, pp. 1-12, 2021.

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