User talk:PhDblackhole

If string theory is a theory of gravity, then what is the relationship between strings, gravitons and spacetime geometry?

Strings and gravitons

The simplest case to imagine is a single string traveling in a flat spacetime in d dimensions. As the string moves around in spacetime, it sweeps out a surface in spacetime called the string worldsheet, a two-dimensional surface with one dimension of space (s) and one dimension of time (t). There are many ways to examine this string theory. One way is to expand the string coordinates Xa(s,t) into oscillator modes and demand spacetime Lorentz invariance and the absence of negative norm states. A different way to examine the string theory is through the field theory defined on the worldsheet, which is described by the action

where hmn is the metric on the worldsheet, R(2) is the curvature of the worldsheet, and F is a scalar field called the dilaton. The consistency condition for string theory when described in this manner is that the field theory on the worldsheet satisfy the condition for scale invariance, also known as conformal invariance. The set of functions that describe the scaling properties of quantum fields are called the beta functions. String worldsheet physics is invariant under a change in scale if the beta function bF for the dilaton field F vanishes, which happens when d=26 for bosonic strings.

(For superstring theories, conformal invariance is replaced by superconformal invariance, and the required spacetime dimension is 10.) The spacetime oscillation spectrum satisfies Lorentz invariance in 26 dimensions, so that these string oscillations on the worldsheet can be classified by the spacetime properties of mass and spin, just like elementary particles. A theory based on open strings has massless oscillations that are Lorentz vectors, with spin 1. A closed string theory is like a product of two open string theories, with an oscillation mode that travels in spacetime as a two index symmetric tensor, with spin 2. This mode with spin 2 propagates like as small fluctuation in the gravitational field propagates according to general relativity. This string oscillation mode should then be the graviton, the particle that mediates the gravitational force. The presence of this spin 2 oscillation mode was the first clue that string theory was not a theory of strong interactions, but a potential quantum theory of gravity.

Strings and spacetime geometry

In string theory, if we start with flat spacetime, we see gravitons in the spectrum, and therefore we deduce that gravity must exist. But if gravity exists, then spacetime must be curved and not flat. How do the Einstein equations for the curvature of spacetime come out of string theory? If a closed string is traveling in a curved spacetime with metric field gab(X), then the string worldsheet theory looks like

The spacetime metric gab(X) enters the two-dimensional theory on the string worldsheet as a matrix of nonlinear couplings between the Xa(s,t). Once again, the goal of conformal invariance is met by demanding that the beta functions vanish. When the string coordinates are expanded in a perturbation series in the string scale a', the terms in the beta functions that are the lowest order in a' contain terms proportional to the Ricci curvature Rab of the spacetime metric field gab(x) and second derivatives of the scalar field F(x). The vanishing of the beta functions ends up being equivalent to satisfying the Einstein equation for a spacetime with a scalar field

at distance scales large compared to the string scale. Notice this means that our understanding of spacetime from perturbative string theory will always be incomplete, except in some special circumstances described below. What about strings and black holes?

Black holes are solutions to the Einstein equation, therefore string theories that contain gravity also predict the existence of black holes. But string theories give rise to more interesting symmetries and types of matter than are commonly assumed in ordinary Einstein relativity. In particular, electric/magnetic duality in string theory has led to the discovery of many new types of black holes with combinations of electric and magnetic charge, coupled to both scalar and axion fields. Also, string theory has motivated an understanding of black holes in higher dimensions, and of black extended objects such as strings and branes. Some of these new stringy extreme black hole solutions possess unbroken supersymmetries at the event horizon, so that the physics at the horizon is protected from higher order perturbative corrections by virtue of supersymmetric nonrenormalization theorems. These types of black holes have been important for understanding the origin of black hole entropy in string theory,and that will be described in the next section.

Is spacetime fundamental?

Note that string theory does not predict that the Einstein equations are obeyed exactly. Perturbative string theory adds an infinite series of corrections to the Einstein equation

So our understanding of spacetime in perturbative string theory is only valid as long as spacetime curvature is small compared to the string scale. However, when these correction terms become large, there is no spacetime geometry that is guaranteed to describe the result. Only under very strict symmetry conditions, such as unbroken supersymmetry, are there known exact solutions to the spacetime geometry in string theory. This is a hint that perhaps spacetime geometry is not something fundamental in string theory, but something that emerges in the theory at large distance scales or weak coupling. This is an idea with enormous philosophical implications.

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'''-- [http://en.wikipedia.org/wiki/User:Riley_Huntley/You_missed! Cheers, ] Ri l ey   ''' 02:34, 3 March 2013 (UTC)

A big complicating factor in understanding string cosmology is understanding string theories. String theories and M theory appear to be limiting cases of some bigger, more fundamental theory. Until that's sorted out, anything we think we know today is potentially up for grabs. That being said, there are some basic issues in string theory cosmology:

1. Can string theory make any cosmological predictions relevant to Big Bang physics? 2. What happens to the extra dimensions? 3. Is there Inflation in string theory? 3. What can string theory tell us about quantum gravity and cosmology?

Low energy string cosmology

Most of the mass in our Universe appears to occur in the form of dark matter. One leading candidate for the composition of this dark matter is something called a WIMP, a Weakly Interacting Massive Particle. One strong candidate for the WIMP comes from supersymmetry. The Minimal Supersymmetric Standard Model (MSSM) predicts the existence of spin 1/2 fermions called neutralinos that are the fermionic superpartners of the neutral gauge bosons and Higgs scalars. Neutralinos would have a high mass but interact very weakly with other particles. They could make up a significant portion of the mass density of the Universe without emitting light, so that makes them good candidates for the mysterious source of dark matter in the Universe. String theories require supersymmetry, so in principle, if neutralinos were discovered to make up cosmic dark matter, that would be good. But if supersymmetry were unbroken, fermions and bosons would be exactly matched in the Universe, and that's not the way things are. The really hard part of any supersymmetric theory is to break the supersymmetry without losing all the advantages of having had the supersymmetry to begin with. (It's very much one of those proverbial cake situations.) One of the reasons particle and string physicists have liked supersymmetric theories is that they predict zero total vacuum energy, because the fermion and boson vacuum energies cancel each other out. When supersymmetry is broken, the fermions and bosons don't exactly match any more, the cancellation doesn't occur any more. There seems to be pretty good evidence from the red shifts of distant supernovae that the expansion of our Universe is accelerating due to something like a vacuum energy or a cosmological constant. So whatever path by which supersymmetry is broken in string theory needs to lead at the end to the right amount of vacuum energy to account for this observed acceleration. This is a theoretical challenge, because supersymmetry breaking seems to give too large a contribution. Cosmology and extra dimensions

Superstring cosmology is enormously complicated by the presence of those pesky six (or seven in the case of M theory) extra space dimensions that are required for quantum consistency of the theory. Extra dimensions that just sit there are challenging enough to deal with in string theory, but in the framework of cosmology, the extra dimensions are evolving in time according to the physics of the Big Bang and whatever happened before it. So what keeps the extra dimensions from expanding to get as big as the three space dimensions that we observe and measure in our Universe? But wait - there's a complicating factor to the complicating factor: a superstring duality symmetry known as T duality. When a space dimension is rolled up in a circle of radius R, the resulting string theory ends up being equivalent to another string theory with a space dimension rolled up in a circle of radius Lst2/R, where Lst is the string length scale. For many of these theories, when the extra dimension radius R satisfies the condition R = Lst, the string theory has an enhanced symmetry with some massive particles becoming massless. This is called the self dual point and has special significance for many reasons. This duality symmetry has led to an interesting proposal for pre-Big Bang cosmology where the stringy Universe starts out flat, cold and very large instead of curved, hot and very small. This early Universe is unstable and starts to collapse and contract until it reaches the self dual point, where it heats up and starts to expand to give the expanding Universe we observe today. One advantage to this model is that it incorporates the very stringy behavior of T duality and the self dual point, so it is a very inherently stringy cosmology.

Inflation vs. the giant brane collision

What does string theory predict for the source of the vacuum energy and pressure necessary to drive the inflationary period of accelerating expansion? Scalar fields that could inflate Universe at GUT scale could also be involved in breaking supersymmetry at just above electroweak scale, determining coupling strengths of gauge fields, and maybe even providing the vacuum energy for a cosmological constant. String theory contains the ingredients to build models with supersymmetry breaking and inflation or quintessence, but the trick is to get all the ingredients to work together, and that is still, as they say, an active area of research. A current alternative model to inflation is the giant brain collision model, also known as the Ekpyrotic Universe, or the Big Splat. This intriguing model starts out with a cold, static five-dimensional spacetime that is close to being perfectly supersymmetric. The four space dimensions are bounded by two three-dimensional walls or three branes, and one of those three-dimensional walls makes up the space that we live on. The other brane is hidden from our perception. According to this theory, there is a third three brane loose between the two bounding branes of the four dimensional bulk, and when this brane hits the brane we live on, the energy from the collision heats up our brane and the Big Bang occurs in our visible Universe as described elsewhere in this site. This proposal is quite new, and it remains to be seen whether it will survive careful scrutiny.

The problem with acceleration

There is a problem with an accelerating Universe that is fundamentally challenging to string theory, and even to traditional particle theory. In eternal inflation models and most quintessence models, the expansion of the Universe accelerates indefinitely. This indefinite acceleration leads to situation where a hypothetical observer traveling forever through the Universe will be eternally blocked from seeing any evidence of most of the Universe. The boundary of the region beyond which an observer can never see is called that observer's event horizon. In cosmology, the event horizon is like the particle horizon, except that it is in the future and not in the past. From the point of view of human philosophy or the internal consistency of Einstein's theory of relativity, there is no problem with a cosmological event horizon. So what if we can't ever see some parts of the Universe, even if we were to live forever? But a cosmological event horizon is a major technical problem in high energy physics, because of the definition of relativistic quantum theory in terms of the collection of scattering amplitudes called the S Matrix. One of the fundamental assumptions of quantum relativistic theories of particles and strings is that when incoming and outgoing states are infinitely separated in time, they behave as free noninteracting states. But the presence of an event horizon implies a finite Hawking temperature and the conditions for defining the S Matrix cannot be fulfilled. This lack of an S Matrix is a formal mathematical problem not only in string theory but also in particle theories. One recent attempt to address this problem invokes quantum geometry and a varying speed of light. This remains, as they say, an active area of research. But most experts doubt that anything so radical is required.