Quantum Memory Burden Effect May Allow Primordial Black Holes to Constitute All Dark Matter

Primordial Black Holes (PBHs), theoretical black holes formed from primordial fluctuations in the early universe, could potentially constitute all or part of the universe’s Dark Matter (DM). The possibility has gained traction following the LIGO detection of merging black hole binaries. Despite no observational evidence for PBHs, constraints have been placed on the fraction of DM they could form. The “memory burden effect,” a quantum effect that alters the evaporation process of black holes, could have significant implications for the mass ranges allowed for PBHs to constitute all of DM, potentially allowing for PBHs in previously excluded mass ranges.

What are Primordial Black Holes and their Role in Dark Matter?

Primordial Black Holes (PBHs) are a theoretical type of black hole that could have formed from primordial fluctuations in the early universe. The possibility of PBHs constituting all or part of the Dark Matter (DM) in the Universe has been considered for some time. This possibility has recently seen a renewed interest due to the LIGO detection of merging black hole binaries with masses around 1-50M, whose formation is not easily explained by astrophysical processes.

Although there is currently no observational evidence for their existence, several constraints have been put on the fraction of DM in the form of PBHs. These constraints are defined as the ratio of the density of PBHs to the density of DM for different values of the PBH mass. Currently, there are only a few mass ranges of interest that still leave the door open for PBHs to constitute all of DM.

An important point of interest is that PBHs are the only ones that can be small enough for Hawking radiation to be relevant. For a PBH forming from primordial fluctuations, its mass should be comparable to the horizon mass at the time of its formation. The standard Hawking evaporation time, which describes the lifetime of a PBH of mass M, can be expressed in terms of the gravitational radius and entropy of the black hole.

How does the Memory Burden Effect Impact PBHs?

The standard semiclassical evaporation scenario, which relies on the assumption of self-similarity, is used to estimate the lifetime of a PBH. That is, during its evaporation, a black hole gradually shrinks in size while maintaining the standard semiclassical relations between its parameters such as its mass, the radius, and the temperature. However, this estimate is based on the semiclassical evaporation scenario, which relies on the assumption of self-similarity.

Recent findings show that the above assumption is not only unjustified but it is actually inconsistent over the long timescales of the evolution. That is, the semiclassical approximation cannot hold throughout the entirety of the black hole lifetime. The first evidence of this came from a microscopic picture which resolves a classical black hole as a coherent state of gravitons. This picture shows that due to the quantum backreaction, any such state must go out of the validity of the semiclassical approximation latest by the time of its half-decay.

What is the Memory Burden Effect?

The memory burden effect is a quantum effect that takes the evaporation process out of the semiclassical regime. This effect is due to the quantum backreaction, which is of order 1/S per emission time, and comes from two effects that go hand in hand. The first one is the loss of coherence generated by the inner entanglement among the constituent gravitons. The second engine, the most relevant for the present paper, is the so-called memory burden effect.

A powerful property of this effect is that it goes beyond a particular microscopic description of a black hole and is generic for systems of high microstate entropy S. Such systems possess an exponentially large number e^S of degenerate microstates which can store large amounts of quantum information. Due to this, systems with S>1 exhibit an enhanced capacity of information storage.

How does the Memory Burden Effect Impact the Mass Window for PBHs?

The memory burden effect has significant implications for the mass ranges allowed for PBHs to constitute all of Dark Matter. These constraints rely on the standard semiclassical approximation, which assumes that the evaporation process is self-similar. However, quantum effects such as memory burden take the evaporation process out of the semiclassical regime latest by half-decay time.

Theoretical evidence based on prototype models indicates that the evaporation slows down, thereby extending the lifetime of a black hole. This modifies the mass ranges constrained in particular by BBN and CMB spectral distortions. The study shows that previous constraints are largely relaxed when the PBH lifetime is extended, making it possible for PBHs to constitute all of DM in previously excluded mass ranges. In particular, this is the case for PBHs lighter than 10^9g, which enter the memory burden stage before BBN and are still present today as DM.