This post lays out the fact that we know almost all of the fundamental laws of physics, and describes what I see as the most plausible resolutions to the ones for which we don't have consensus answers.
We Understand The Particle Physics Of Everything But The First Fraction Of A Second After The Big Bang
In the standard chronology of the universe in cosmology, there is a state change from quark-gluon plasma to confined hadrons (mostly protons and neutrons) at one second after the Big Bang.
This is only a rough approximation, however. The physics of the Standard Model up to this temperature (about 5.5 trillion degrees Kelvin) have been experimentally confirmed at the Large Hadron Collider. More exactly, this temperature, where the quark-gluon plasma state change is expected ends at 10^-12 seconds after the Big Bang, in the standard chronology of the universe, dramatically shrinking the time period in the universe where we don't fully understand the relevant particle physics from the first second, to the first trillionth of a second. The trillionth of a second in the history of the universe where the Standard Model has not been experimentally confirmed is one part per 10^30 of the time that the universe has existed.
The Standard Model is mathematically consistent and sound for at least another twenty-two orders of magnitude beyond that point (i.e. up to the GUT scale), to one part per 10^52 of the time that the universe has existed, but hasn't been experimentally tested in the higher energy parts of that domain.
The hypothetical Planck epoch, which is a point where the Standard Model equations might break down, is about three orders of magnitude smaller in the time after the Big Bang. The Planck time, a dimensional reasoning based theoretical possible minimum unit of time, is about 10^-43 seconds and would be characterized by energy scales of 10^19 GeV or greater. Classical general relativity predicts a gravitational singularity before this point, although a quantum gravity theory might not have a singularity.
This chronology assumes that Big Bang Nucleosynthesis with the newly formed protons and neutrons begins about ten seconds after the Big Bang and lasts for about sixteen and a half minutes. The particle and nuclear physics of Big Bang Nucleosynthesis are scientifically well understood, and the predictions of the BBN model are confirmed with observations, subject to some modest discrepancies in lithium levels that recent astronomy observations have tended to confirm by finding missing lithium levels and better modeling lithium production and destruction during the 13.7 billion years between the end of BBN and the present in nuclear reactions in stars.
So, any "new physics" that arise at energies above those that the Large Hadron Collider could reach are restricted to some fraction of the first second of the Universe. We fully understand the laws of physics (except dark matter and dark energy and possibly quantum gravity) that apply in the circumstances found in the universe at all time after that.
There are three main possible kinds of "new physics" motivated by astrophysics that scientists are looking for, and one kind of unobserved Standard Model physics that hasn't been observed because energies are too low, that could be restricted to the high energies found only in the first second after the Big Bang. They are, respectively: Cosmological inflation, baryogenesis, leptogenesis, and baryon number and lepton number non-conserving (but B-L preserving) sphaleron interactions.
Sphaleron interactions, while theoretically interesting, aren't enough to explain baryogenesis or leptogenesis, or any other phenomena in the world later than a fraction of a second after the Big Bang, so while undiscovered and theoretically interesting, are basically a side curiosity. These also require temperatures about 100 times the hottest temperature reached at the LHC, so the time frame in which they could have occurred is significantly less than a trillionth of a second.
The cosmology narrative that I find most plausible, mirror cosmology, simultaneously eliminates the need for cosmic inflation, explains the baryon asymmetry of the universe without post-Big Bang new physics, and answers the question "how could something come out of nothing" at least partially by causing the Big Bang to no longer violate mass-energy conservation.
Deur's approach to gravity meanwhile, eliminates the need for either dark matter or dark energy, and solves all or many of the problems with the LambdaCDM Standard Model of Cosmology, and has been explored preliminarily not just at the scale of galaxies and galaxy clusters, but also in cosmology applications. He also eliminates the mass-energy conservation exception (the only one in physics other than the Big Bang itself) associated with dark energy by a means that I've not seen utilized by any other theory in astrophysics.
Baryogenesis and Leptogenesis
The baryon asymmetry of the universe (i.e. the vast excess of protons and neutrons over anti-protons and anti-neutrons) requires one of two things:
(1) the large positive net baryon number of the Universe (i.e. the excess of protons and neutrons over anti-protons and anti-neutrons) was present essentially at the outset of the Big Bang, or
(2) the Big Bang started with matter and antimatter in perfect balance and sometime in the first second after the Big Bang, a baryon number non-conserving process that violates CP conservation much more strongly than any process in the Standard Model exists at energies higher than those in the Standard Model generating the asymmetry seen today.
Mirror cosmology, in which there is an anti-matter universe before the Big Bang in time, and our matter universe after it, explains baryogenesis and leptogenesis without new physics and basically allows the Universe as a whole to have equal amounts of matter and antimatter, while not requiring a new charge parity (CP) violating process not found in the Standard Model at high energies (except for a time bias between matter and antimatter in pair production of quarks and leptons at the time of the Big Bang).
As quarks and antiquarks are photoproduced at the Big Bang, the quarks disproportionately end up on our side of the Big Bang, and the antiquarks disproportionately end up before the Big Bang in time.
As charged leptons and charged antileptons are photo-produced at the Big Bang, the charged leptons disproportionately end up on our side of the Big Bang and the anti-leptons disproportionately end up before the Big Bang in time.
Neutrinos, by the way, aren't photoproduced because they don't have an electromagnetic charge. So, the neutrinos in our post-Big Bang observable universe, would all be created post-Big Bang in lepton number conserving interactions. And, while beta decay can create an electron and an anti-neutrino, given what we know about the frequency of beta decay and the proportion of protons and neutrons in the universe, the net lepton number of the universe should be at least similar to the number of charged leptons in the universe (which is almost identical to the number of protons in the universe), while the number of anti-neutrinos should only slightly and imperceptibly exceed the number of neutrinos in the our observable universe.
Cosmological Inflation
Cosmological inflation is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from 10^−36 seconds after the conjectured Big Bang singularity to some time between 10^−33 and 10^−32 seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate.
Inflation presumes an expansion of space at faster than the speed of light in this time period. At the speed of light, in 10^−32 seconds, light moves 10^−24 meters (by comparison a proton is about 10^−15 meters across). But, in one typical inflation theory, space expands from a 10^-50 meter radius at 10^-35 seconds after the Big Bang to about a 1 meter radius at 10^-34 seconds.
These new inflation physics purportedly appear so early on in this scenario, that the entire universe would fit in my bathroom with room to spare. The energy scale at which this is supposed to happen is the GUT scale, i.e. about 10^15 GeV to 10^16 GeV.
Put another way, cosmological inflation is a one time fix that ends when the universe has a one meter radius in the first 10^-34 seconds after the Big Bang, or so, so it is functionally just a set of hypothesized initial conditions of the universe from that moment slightly after the Big Bang.
The Wikipedia article on Cosmic Inflation explains:
The detailed particle physics mechanism responsible for inflation is unknown. The basic inflationary paradigm is accepted by most physicists, as a number of inflation model predictions have been confirmed by observation; however, a substantial minority of scientists dissent from this position. The hypothetical field thought to be responsible for inflation is called the inflaton.
There are literally hundreds of proposed inflation theories (a 300 page summary of the various inflation theories can be found here) and astronomy observations have time and again narrowed the parameter space of potential inflation theories to rule out a great many of them. See, e.g., prior posts from this blog on March 21, 2013, March 18, 2014, July 24, 2017, and October 4, 2021. In the first of those posts, I noted that:
Planck [cosmic microwave background observations] strongly disfavors power law inflation, the simplest hybrid inflationary models, simple monomial models with n > 2, single fast roll inflation scenarios, multiple stage inflation scenarios, inflation scenarios with flat or concave potentials, dynamical dark energy, time variations of the fine structure constant are all strongly disfavored. Any theory that would create non-Gaussian statistics of the CMB anisotropies, non-flat universes, tensor modes, or statistically discernible deviations from isotropy at L >50 are ruled out.
The summary chart from the 2021 paper is as follows:
Only the blue part of the parameter space remains open, so "natural inflation" is ruled out.Many people (including many serious astrophysicists and me) are skeptical that cosmic inflation is really necessary. In an October 31, 2016 post, I noted that even one of inflation theory's original creators doubts that it really exists.
Paul Steinhardt gave a colloquium at Fermilab last month with the title Simply Wrong vs. Simple. In it he explained “why the big bang inflationary picture fails as a scientific theory” (it doesn’t work as promised, is not self-consistent and not falsifiable).
Deur's gravitational work is agnostic on the subject.
An abstract of a paper on the topic of mirror cosmology also explains the basic astronomy motivation for cosmic inflation, and why the mirror cosmology model dispenses with the need for it.
Observations indicate that the early Universe was strikingly simple: a fraction of a second after the Big Bang, the Universe was radiation-dominated, almost perfectly homogeneous, isotropic, and spatially flat; with tiny (around 10^−5) deviations from perfect symmetry also taking a highly economical form: random, statistically gaussian, nearly scale-invariant, adiabatic, growing mode density perturbations.
Although we cannot see all the way back to the bang, we have this essential observational hint: the further back we look (all the way back to a fraction of a second), the simpler and more regular the Universe gets. This is the central clue in early Universe cosmology: the question is what it is trying to tell us.
In the standard (inflationary) theory of the early Universe one regards this observed trend as illusory: one imagines that, if one could look back even further, one would find a messy, disordered state, requiring a period of inflation to transform it into the cosmos we observe.
An alternative approach is to take the fundamental clue at face value and imagine that, as we follow it back to the bang, the Universe really does approach the ultra-simple radiation-dominated state described above (as all observations so far seem to indicate).
Then, although we have a singularity in our past, it is extremely special. Denoting the conformal time by τ , the scale factor a(τ) is ∝ τ at small τ so the metric g^(µν) ∼ a(τ)^(2ηµν) has an analytic, conformal zero through which it may be extended to a “mirror-reflected” universe at negative τ.
[W]e point out that, by taking seriously the symmetries and complex analytic properties of this extended two-sheeted spacetime, we are led to elegant and testable new explanations for many of the observed features of our Universe including: . . . (ii) the absence of primordial gravitational waves, vorticity, or decaying mode density perturbations; (iii) the thermodynamic arrow of time (i.e. the fact that entropy increases away from the bang); and (iv) the homogeneity, isotropy and flatness of the Universe, among others.
The Dark Sector
Deur's work on gravity, purports to explain the phenomena attributed to dark matter and dark energy with non-perturbative weak field gravitational effects. Other gravity based approaches (e.g. here) likewise seek to explain dark matter and dark energy without new particles or substances, in various ways, one of the most notable of which adds conformal symmetry to the constraints of general relativity.
In my opinion, the balance of the evidence strongly favors either some gravitational explanation for dark matter or an ultralight bosonic dark matter particle with a mass-energy on the same order of magnitude as a graviton that looks a lot like a fifth force.
One of the strongest pieces of evidence that dark matter, if it exists, must be very light is Alfred Amruth, "Einstein rings modulated by wavelike dark matter from anomalies in gravitationally lensed images" Nature Astronomy (April 20, 2023) https://doi.org/10.1038/s41550-023-01943-9 (Open access copy available at arxiv).
And, the gravitational approach is better motivated in y humble opinion, and has more rigorously been confronted with the evidence.
Deur's approach to gravity is more intuitive in a graviton based quantum gravity context, but he claims that it works in unmodified classical general relativity (without a cosmological constant) as well if non-perturbative effects are considered.
If Deur is correct, there is about 95% less mass-energy in the universe than expected in the LambdaCDM Standard Model of Cosmology, and there is no observational motivation for stable particles not explained by the Standard Model of Particle Physics (other than gravitons) to exist.
Mass-Energy Conservation
By eliminating the need for dark energy, Deur also removes the one exception to conservation of mass-energy in general relativity (and physics generally) that dark energy creates, except at the moment of the Big Bang when you have a "something created out of nothing" issue. This is solved at the moment of the Big Bang in mirror cosmology.
Quantum Gravity
Another benefit of removing the cosmological constant from general relativity is that it makes it easier to formulate a quantum gravity theory if you don't need to include the Lambda (i.e. cosmological constant) term from Einstein's field equations (which incidentally is a gravitational explanation for dark energy).
This isn't the biggest barrier to a quantum gravity theory, however. The biggest barrier is that general relativity isn't renormalizable, which is a property that any usable and non-pathological theory of quantum gravity should have, at least not perturbative the way that the three Standard Model forces are.
But, it looks like the same approach the Deur took to explain dark matter and dark energy phenomena, non-perturbative effects of general relativity, also make general relativity non-perturbatively renormalizable. This suggest a roadmap for finally crossing the seemingly insurmountable barrier of mathematically formulating a quantum gravity theory.
There are, however, quite strict observational constraints on quantum gravity effects.
If quantum gravity does exist, the gravitational coupling constant has a beta function that explains how it runs with energy scale, which could also provide useful insight and ought to be possible to devise from first principles. One effort to do so is mentioned here.
The existence of quantum gravity would also slightly tweak the beta functions of the other Standard Model experimentally measured physical constants, which might have interesting implications at very high energies.
Neutrinos
Science still need to pin down some of the physical constants associated with neutrinos (which is just a matter of brute force effort and isn't theoretically problematic) and the nature of neutrino mass (Majorana or Dirac). I strongly suspect that neutrinos have Dirac mass and have some ideas about where it comes from (basically, through W boson and/or Z boson mediated interactions and self-interactions).
Explaining the Standard Model Constants
The only other thing we don't know in physics that would be nice to know (although it isn't strictly necessary to explain the observed universe) is the way that the physical constants for the fifteen experimentally measured masses of the Standard Model (which are only fourteen degrees of freedom because the W and Z boson masses are functionally related to each other in the electroweak theory of the Standard Model), the eight parameters of the CKM matrix and the PMNS matrix, and the three Standard Model coupling constants (as well as Newton's constant, Planck's constant, and the speed of light). The electromagnetic and weak force coupling constants are also functionally related to each other and to the W and Z boson masses.
There is good reason to believe that a "within the Standard Model" theories could explain a great many of these physical constants a derived values rather than just experimentally measured physical constants.
The masses of the Standard Model fundamental particles, which have origins in the electroweak sector of the model, seem particularly susceptible to being explained this way, that I've explored in prior posts at this blog. Basically, I think that Koide's rule and extensions of this point to the Yukawa couplings to the Higgs field having their roots in dynamic balancing of these values through W boson interactions. The LP & C relation suggests a connection between the Higgs vacuum expectation value (which is a function of the W boson mass and the weak force coupling constant) is the source of the overall mass scale of the fundamental particles of the Standard Model.
It might also be possible to reduce the number of non-derived CKM matrix parameters from four to two with a little more theoretical work, and maybe someday, similar progress could be made with the four PMNS matrix parameters.
These efforts wouldn't bring the number of experimentally measured fundamental physical constants in the Standard Model to zero or even to one, but it might be possible to get them down, perhaps, from twenty-five to eight (plus the speed of light, Planck's constant, and Newton's constant).
Fourth Generation (Or Greater) Standard Model Fermions
It is very unlikely that there are fourth generation fundamental fermions. Instead, there are exactly three generations of Standard Model fermions.
For theoretical reasons, there has to be a full set of an up-type quark, down-type quark, charged lepton, and neutrino in each generation.
Direct searches and cosmology observations rule out these possibilities up to high masses relative to the third generation. This is particularly in the case of a four generation active Standard Model neutrino; which has been ruled out to, at least, 45,000,000,000 eV (the heaviest of the three Standard Model neutrino masses is not more than 2 eV by direct measurements and neutrino oscillation data, and is less than 0.1 eV based upon cosmology bounds). Fourth generation down type quarks are ruled out up to 3,000 GeV by direct searches (the b quark mass is about 4.2 GeV). Fourth generation up type quarks are ruled out up to 1,500 GeV by direct searches (the t quark mass is about 173 GeV). Fourth generation charged leptons are ruled out up to 100.8 GeV by direct searches (the tau lepton mass is about 1.78 GeV).
Also, from a theoretical perspective, a fourth generation or higher Standard Model fermion more massive that then top quark is ruled out because its expected mean lifetime would be shorter than the mean lifetime of the W boson that effects its decay. The mean lifetimes of the W and Z bosons, which are the most short-lived particles ever observed, are each about 3*10^-25 seconds. The mean lifetime of the top quark is about 5*10^-25 seconds, which is the shortest of the Standard Model fermions and is so short that top quarks decay before they can hadronize.
Furthermore, the existence of fourth generation fundamental Standard Model fermions would cause the decays of the Standard Model Higgs boson to differ greatly from what is observed.
The Strong CP Problem
I also have my own heuristic answer to the strong CP problem, which is that since gluons that mediate the strong force are massless and thus don't experience time in their own reference frame, that neither gluons, nor any other massless particles, can experience CP violation which is equivalent to time symmetry violation.
This makes a hypothetical axion particle to suppress CP violation in strong force interactions unnecessary.
