Modified Friedmann Equations via Conformal Bohm–de Broglie Gravity

Abstract

We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background metric. We apply this method to the Robertson-Walker metric to derive a modified version of Friedmann's equations for a Universe consisting of scalar, spinzero, massive particles. These modified equations include additional terms that result from the nonlocal nature of matter and appear as an acceleration in the expansion of the Universe. We see that the same effect may also be present in the case of an inhomogeneous expansion.

Towards a quantum fluid theory of correlated many-fermion systems from first principles

“…These approaches are based on an observation made by de Broglie pointing out that quantum mechanical effects are entirely equivalent to a conformal transformation of the background metric [48,49]. This leads to a representation of the non-local Bohm potential of all the particles in the Universe as an effective cosmological constant [21]. Therefore, this outlines an interesting line of future research.…”

“…One such method is quantum hydrodynamics (QHD). There has recently been a surge of activities based on QHD in a number of research areas including warm dense matter (WDM) [10][11][12][13], plasmonics [14][15][16], electron transport in semiconductor devices and thin metal films [17,18], reactive scattering [19,20], cosmology, and dark matter research [21][22][23].…”

Note on Dark Energy and Cosmic Transit in a scale-invariance cosmology

“…where ds ′ is the line element of general relativity and ds is the line element of a more general space [33]. Although some modified scale-invariance gravity theories have been introduced to explain the cosmic acceleration [29,30,32], the ability of the scale-invariance cosmological models to provide a complete description to cosmic evolution still not confirmed.…”

“…where r, θ, φ are comoving spatial coordinates, a(t) is the cosmic scale factor, t is time, κ is either 0, −1 or +1 for flat, open and closed universe respectively. In [32], the conformal transformations…”

Disformal transformations and the motion of a particle in semi-classical gravity

“…In that case one has to take an ansatz for the vector field different from the one given here 11. This approach was recently used in[23] to derive a quantum version of the Friedmann equations.…”