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E. G. M. Ferreira
problematic since its smallness is vexing given its radiative instability under
quantum corrections [4]. On small scales, a number of challenges have emerged
for this hydrodynamical description of the CDM [5], with the most striking being
the scaling relations like the mass discrepancy acceleration relation (MDAR), which
correlates the dynamical gravitational acceleration inferred from rotation curves and
the gravitational acceleration due to baryons only [6, 7].
There is a debate about the explanation for these curious relations on small scales.
Within ΛCDM model it is claimed that it can be solved by the inclusion of baryonic
feedback effects in simulations (see [8] for a review). An alternative is to modify
the behavior of DM on small scales while maintaining the successes of CDM on
large scales. Ultra-light fields have emerged as an alternative DM scenario with a
different mechanism to explain the dynamics on small scales where DM forms a
Bose–Einstein condensate (BEC) or a superfluid in galaxies (for a review [8] of this
class of models). One model that accomplishes that is the DM superfluid [9, 10],
where sub-eV mass particles with sufficiently strong self-interactions thermalize
and condense in galaxies. On top of that for a certain superfluid equation of state
and in the presence of coupling of the DM phonons to baryons, this theory’s effective
Lagrangian is similar to the MOND scalar field theory [11] that leads to a modified
dynamics inside galaxies similar to Milgrom’s empirical law 1 [12] known to explain
and predict these scaling relations.
An interesting question is if the late-time cosmic acceleration can also emerge in
the DM superfluid framework, as yet another manifestation of the same underlying
substance. We show here that it is indeed possible if we consider that the DM is
composed by a mixture of two superfluids, which can be in two different states of the
same superfluid, that are in contact and interacting through a contact Josephson-like
interaction [13], converting one species into the other. For the phonons that describe
the superfluid this interaction appears as an oscillatory potential that drives the latetime acceleration. The unified vision of the dark sector is attractive for its simplicity,
given that in this model needs DM in the form of a superfluid alone to describe both
the DM behavior on large and small scales, and the late-time acceleration.
The DM superfluid model and the unified framework present a series of
observational consequences [9, 10, 14] that successfully explain some observational
challenges in galactic dynamics, cosmological evolution or present new interesting
phenomenological consequences.
1 This empirical law states that the total gravitational acceleration a is approximately the Newtonian
acceleration a N due to baryonic matter alone, in the regime a N a 0 , and approaches the geometric
mean
√
a N a 0 whenever a N λa 0 .
E. G. M. Ferreira
problematic since its smallness is vexing given its radiative instability under
quantum corrections [4]. On small scales, a number of challenges have emerged
for this hydrodynamical description of the CDM [5], with the most striking being
the scaling relations like the mass discrepancy acceleration relation (MDAR), which
correlates the dynamical gravitational acceleration inferred from rotation curves and
the gravitational acceleration due to baryons only [6, 7].
There is a debate about the explanation for these curious relations on small scales.
Within ΛCDM model it is claimed that it can be solved by the inclusion of baryonic
feedback effects in simulations (see [8] for a review). An alternative is to modify
the behavior of DM on small scales while maintaining the successes of CDM on
large scales. Ultra-light fields have emerged as an alternative DM scenario with a
different mechanism to explain the dynamics on small scales where DM forms a
Bose–Einstein condensate (BEC) or a superfluid in galaxies (for a review [8] of this
class of models). One model that accomplishes that is the DM superfluid [9, 10],
where sub-eV mass particles with sufficiently strong self-interactions thermalize
and condense in galaxies. On top of that for a certain superfluid equation of state
and in the presence of coupling of the DM phonons to baryons, this theory’s effective
Lagrangian is similar to the MOND scalar field theory [11] that leads to a modified
dynamics inside galaxies similar to Milgrom’s empirical law 1 [12] known to explain
and predict these scaling relations.
An interesting question is if the late-time cosmic acceleration can also emerge in
the DM superfluid framework, as yet another manifestation of the same underlying
substance. We show here that it is indeed possible if we consider that the DM is
composed by a mixture of two superfluids, which can be in two different states of the
same superfluid, that are in contact and interacting through a contact Josephson-like
interaction [13], converting one species into the other. For the phonons that describe
the superfluid this interaction appears as an oscillatory potential that drives the latetime acceleration. The unified vision of the dark sector is attractive for its simplicity,
given that in this model needs DM in the form of a superfluid alone to describe both
the DM behavior on large and small scales, and the late-time acceleration.
The DM superfluid model and the unified framework present a series of
observational consequences [9, 10, 14] that successfully explain some observational
challenges in galactic dynamics, cosmological evolution or present new interesting
phenomenological consequences.
1 This empirical law states that the total gravitational acceleration a is approximately the Newtonian
acceleration a N due to baryonic matter alone, in the regime a N a 0 , and approaches the geometric
mean
√
a N a 0 whenever a N λa 0 .