Mimetic Dark Matter

Abstract: We reformulate Einstein's theory of gravity, isolating the conformal degree of freedom in a covariant way. This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first derivatives. The resulting equations of motion split into a traceless equation obtained through variation with respect to the auxiliary metric and an additional differential equation for the trace part. As a result the conformal degree of freedom becomes dynamical even in the absence of matter. We show that this extra degree of freedom can mimic cold dark matter.

• The paper demonstrates that isolating the conformal degree of freedom via a scalar field can effectively mimic cold dark matter in Einstein’s gravity.
• The authors derive modified motion equations that include an additional term behaving like a dust energy-momentum tensor in cosmological models.
• The study proposes coupling the scalar field with an inflaton during cosmic inflation to stabilize dark matter density and explore observational implications.

An Evaluation of Mimetic Dark Matter Theory

This paper, authored by Ali H. Chamseddine and Viatcheslav Mukhanov, explores a novel reformulation of Einstein's general relativity that introduces an additional degree of freedom capable of mimicking cold dark matter, termed "mimetic dark matter." The analysis focuses on isolating the conformal degree of freedom in a covariant manner through the use of a scalar field and auxiliary metrics.

The reformulation presented establishes a physical metric as a function of an auxiliary metric and a scalar field. The primary transformation involves expressing the physical metric $g_{\mu\nu}$ through the auxiliary metric $\tilde{g}_{\mu\nu}$ and a scalar field $\phi$ such that conformal invariance is retained. The action integral is invariant under conformal transformations, allowing the conformal degree of freedom to become dynamical even in the absence of conventional matter.

The equations of motion derived from the action include an additional term that is constructed to imitate an energy momentum tensor with characteristics analogous to dust—a form of matter that exerts gravitational influence but doesn't exhibit pressure. This additional term is interpreted as mimetic dark matter, described here as an emergent scalar field within the gravitational field equations.

The conformal invariance introduces an extra scalar degree of freedom, which the authors identify as a potent imitator of cold dark matter. This scalar field satisfies the Hamilton-Jacobi equation for unit mass relativistic particles in a gravitational field, further confirming its role within the mimetic framework. The translational velocity of this mimetic matter is dictated by the scalar field, which aligns with the velocity potential, thus allowing mimetic dark matter to function similarly to classical dark matter within the Universe's gravitational architecture.

In cosmological models, particularly the flat Friedmann universe, the mimetic dark matter is equivalent to a dark matter density determined by an arbitrary constant of integration. This capability allows the phenomena of gravitational instability to be replicated, with mimetic dark matter behaving analogously to classical cold dark matter under gravitational influence while remaining free from interactions known with any standard model particles.

One limiting factor highlighted is the requirement of model modifications in an inflationary framework, where standard mimetic dark matter dynamics would become negligible after extended inflation. The paper proposes coupling the scalar field with an inflaton field during cosmic inflation to stabilize the mimetic dark matter density. This coupling, though significant during inflation, decreases over time, preserving its post-inflationary contributions without decaying completely.

The implications of this mimetic approach to dark matter are multifaceted. Theoretically, it presents an alternative mechanism by which dark matter characteristics might emerge from fundamental gravitational principles without invoking additional particles. Practically, this framework suggests a method for introducing dark matter phenomena directly into existing gravitational models without additional hypothesized unknown matter.

Further developments are anticipated to explore the cosmological implications of this theory, particularly in structure formation and cosmic microwave background fluctuations. Discovering observational evidence supportive of mimetic dynamics or any deviations thereof could lead to significant revisions in our understanding of dark matter and the fabric of the Universe. Future research might also examine the intersection of mimetic theory with other scalar-tensor frameworks, expanding the scope of gravitational theories.

The mimetic dark matter concept addresses an intriguing aspect of modern cosmology: the unexplained visible impact of dark matter components within the Universe's structure. By integrating this into Einstein's theory in a conformally invariant manner, this paper introduces a potentially fertile domain for advancing the current theoretical paradigm.