LyX ⇒ Setting Up LyX to output to PDF, etc.

[astroryan7]

Ok, so I'm sure this has to be a sticky somewhere, but I'm new to LyX (LaTeX) and the forum. I used LyX at one point last semester to write a paper, and had everything configured correctly in terms of viewing as DVI, PDF, etc.

But now I've come to use it again, and when I click "View PDF", I get the message "Undefined control sequence". Is there a quick fix to this? I honestly don't remember how I configured it all the first time. Any help is most appreciated. Thanks.

-Ryan

[Stefan Kottwitz]

Hello Ryan,

welcome to the LaTeX Community board!
Undefined control sequence sounds like there's a problem in the document code. Do you include eps files? Do you use postscript, like pstricks, or at least a dvips option? That could cause problems after switching to pdflatex.
Do you also get errors if you try LyX "View PDF" with just a small new document with some blindtext?
Can you post a .log file of a document with that error? Or even a document.lyx, where the error occures?

Stefan

[astroryan7]

Good call on trying to view a different document; that worked. *facepalm* So, it must be something weird within my document then. But I don't know what you mean by those options (eps, pstricks, dvips); yeah, I'm really new. The document pretty much has standard text (with sections/subsections), a table, a couple figures, and some math.

But I wouldn't mind posting a .log or .lyx file if you tell me how

Thanks
-Ryan

[Stefan Kottwitz]

Hi Ryan,

if you want to post a document, then look below the edit text field, there is an area Upload attachment. In it you can see Filename, click on the button next to it, browse to your lyx file, and the button add the file.

Small documents you can post just inside the normal text. For this it's good to press the Code button above the edit text field.
In general you may find that you may get quicker and more specific answers and solutions if you provide code in detail.

Stefan

[astroryan7]

Stefan,

Here is a copy/paste of my document. I tried uploading it as an attachment, but it says .lyx extensions are not allowed. If you have another suggestion of how to upload it, just let me know (there is a lot of text here, so don't feel obligated to peruse it all; I don't even know if it copied right, but I did select "Code" from above).

Many thanks in advance; I'll be in and out.

-Ryan

Code: Select all

Bianchi Cosmology

1 Introduction

Since the birth of general relativity around 100 years ago, many models of the evolution of the universe have come and gone. We've seen static universes in the form of steady-state theory, universes that collapse and rebirth new universes in the form of brane cosmology, and singularity oringating expanding universes in Big Bang theory. Many theoretical physicists have spent their careers developing the mathematical foundation for these models; and thus, it takes a well-trained mind to fully understand these physical theories. So, the focus of this paper is on the physical interpretations of some of the many models for anisotropic evolution of the early universe. In a 1918 paper, the Italian mathematician Luigi Bianchi classified real Lie algebras into 9 groups, based on such properties as invariant volumes, topological connectedness, and isomorphism. The extension to general relativity allows for the analysis of spatial homogeneity and isotropy on cosmological scales. But perhaps the key reason these models are so appealing in general relativity is that they reduce the partial differential field equations to ordinary differential equations, allowing for the application of many standard mathematical techniques. Table 1 below summarizes the key features of some of these Bianchi groups. Note that some of the most often studied Bianchi cosmologies, and the ones of focus in this paper, are Types I, V, and IX, which represent spatially homogeneous models.

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Some classes of Bianchi groups are omitted from this table due to irrelevance for this paper. See Ryan and Shepley (1975) for further reading. In general, the higher up in the Bianchi classification hierarchy, the more free parameters there are, and thus the more general the model. The Bianchi Type VII model then is the most general of the ``flat'' FRW models; yet, the Bianchi Type I model is more often studied due to its lack of tilt.

2 Observational evidence for anisotropy

Early ground-based and balloon measurements of the cosmic microwave background radiation, discovered in 1965 (Penzias and Wilson, 1965), showed isotropy to within a few parts per thousand (Partridge, 1974). These measurements were often carried out at single declinations and mostly neglected such contributions as the motion of the solar system throughout the Milky Way as well as the large scale motion of the galaxy throughout the supercluster. But more recent observations from the COBE, and later WMAP satellites, and other experiments have shown anisotropy of the CMB on the microkelvin scale, taking all of these effects into consideration (Bennett et al, 1996 and Hanany et al, 2000).





Data show that our group of galaxies is moving at around 600 km/s relative to the CMB in a specific galactic direction (Kogut et al, 1993). This motion results in a blue-shifted spectrum in the direction of motion and red-shifted elsewhere and is explained with simple velocity shifts. However, cosmological models can explain a fraction of the observed dipole temperature shifts in the CMB, as will be discussed below.

Several other observations seem to suggest a preferred direction in the universe. In a 1982 issue of Nature, Birch provided evidence from position angles and polarization of distant radio sources for a rotating universe. Others (Berera et al, 2003) have argued for universal anisotropy due to a background magnetic field. However, no observations outside of the CMB temperature fluctuations have concrete evidence and are not discussed in the rest of this paper.

3 Bianchi Cosmological Models

Anisotropies in the CMB support the argument that the universe began slightly irregular. Scientists have studied this problem largely from two approaches, namely by analyzing small perturbations from the symmetric FRW models and allowing large deviations from this symmetry in only a few degrees of freedom.

This latter approach uses the anisotropic Kasner metric,

ds^{2}=-dt^{2}+t^{2p_{1}}dx^{2}+t^{2p_{2}}dy^{2}+t^{2p_{3}}dz^{2}which is a vacuum solution to the field equations. In this metric, the constants p_{i} satisfy

p_{1}+p_{2}+p_{3}=p_{1}^{2}+p_{2}^{2}+p_{3}^{2}=1

This model portrays an expanding universe, since the volume element \sqrt{-g}=t is constantly increasing in absolute magnitude. Specifically, distances parallel to the x-axis expand at a rate proportional to t^{p_{1}}, while distances parallel to the y and z-axes expand proportional to t^{p_{2}} and t^{p_{3}}, respectively (Misner et al, 1973). Note that the constraint given by the equation above requires that one of the expansion rates p_{i} be non-positive; thus, distances along one axis actually contract. As a result, observers will see blue-shifted radiation along one axis and the same radiation but red-shifted along all other directions. Obviously, this metric is a more generalized model for the directional behavior of the universe.

The usefulness of the Kasner metric is evident in investigation of singularities of the spatially homogeneous models. At least one timelike geodesic is incomplete in this model in which R_{\mu\nu}k^{\mu}k^{\nu}>0for all timelike and null vectors k, (MacCallum, 1979). As long as matter can be ignored near the singularity, the Kasner metric can be used as an approximation, so that Bianchi I universes have a singularity of infinite density. Then, it follows that there would be a universe admitting an isometry group of the same Bianchi type, but acting on timelike surfaces (i.e. a stationary solution of the Einstein field equations). Note that if matter cannot be neglected, the Kasner model becomes “isotropic in old age” (Misner et al, 1973), reducing asymptotically to the flat, homogeneous, isotropic model.

As stated earlier, the most often studied cosmologies are the Bianchi Types I, V, and IX models. The spatially homogeneous and isotropic FRW (Friedmann-Robertson-Walker) model is a subset of these cosmologies, with Types I, V, and IX representing flat, open, and closed universes, respectively. 

3.1 Bianchi Type I Model

These are the simplest anisotropically expanding universe models. The metric is given by

ds^{2}=-dt^{2}+X^{2}(t)dx^{2}+Y^{2}(t)dy^{2}+Z^{2}(t)dz^{2}where the average expansion scale factor is S(t)=(XYZ)^{1/3}. This generalization of the flat FRW model allows for separate expansions in orthogonal directions and is simply transitive on spacelike surfaces (t = constant). It can be shown (Lachièze-Rey, 1999) that the scale factors evolve as:

X(t)=S(t)\left(\frac{t^{2}}{S(t)^{3}}\right)^{\frac{2}{3}sin\alpha_{1}}

Y(t)=S(t)\left(\frac{t^{2}}{S(t)^{3}}\right)^{\frac{2}{3}sin\alpha_{2}}

Z(t)=S(t)\left(\frac{t^{2}}{S(t)^{3}}\right)^{\frac{2}{3}sin\alpha_{3}}where \alpha is a constant. Thus, at late times this isotropizes to give the Einstein de-Sitter model and can be an accurate model of the universe, provided the curvature constant is appropriately chosen.

The Bianchi Type I model succeeds in damping out anisotropy through time. Another way to show this is through the evolution of an arbitrary, yet time-dependent scalar \Omega. Note that Misner (1968) has shown anisotropy to be a function of n_{i}\sigma_{ij}n_{j}, where n_{i} is a unit vector in the direction of observation and \sigma_{ij} is a complicated function of \beta_{ij}, the cosmic expansion parameter. Through the use of a Hamiltonian formulation in the Bianchi Type I model, one can show (Ryan and Shepley, 1975) that the scalar quantity \Omega, where \sigma_{ij} \propto \exp\left[6\Omega\right], is a monotonically decreasing function of time. It follows then that as \Omega decreases, so too does anisotropy; this decay may be an explanation for the largely observed isotropy of the CMB today.

One important consequence of the singularities encountered above is the horizon effect, or the farthest distance an observer can see. Denoting time t_{1} as observer time and time t_{0} as time of the initial singularity, the horizon then depends on the difference t_{1}-t_{0}, not the spatial position of the observer. It can then be shown (Ryan and Shepley, 1975) that the coordinate of the horizon is

\chi^{i}(t_{1})=\intop_{t_{0}}^{t_{1}}e^{\Omega}e^{-\beta_{ii}}dtwhere \Omega and \beta_{ii} represent the earlier defined quantities. The figure below shows the horizon length for an observer A at time \tau. If the horizon size is finite at time t_{1}, then \chi^{i}(t_{1})\rightarrow0 as t_{1}\rightarrow t_{0}. This shows that near the singularity in the Bianchi Type I model, matter can only be influenced by its nearest neighbors. But at the present time \tau, because of the expansion of the horizon, an observer is continually being influenced by new stars (Ryan and Shepley, 1975). This horizon effect is removed for the Type IX model discussed below. 





3.2 Bianchi Type V Model

Some remarks about the characteristics of the Bianchi Type V universe are warranted here. As mentioned earlier, the metric corresponds to a spatially homogeneous, anisotropic, open universe. This differs from the Type I model in that a low observed value for the density of luminous matter is accepted, and thus the universe will expand forever; this is often termed the Big Rip, as opposed to the long held belief of a Big Crunch, or inevitable universal recollapse. Recent evidence (Perlmutter et al, 1998) through observations of Type Ia supernovae, which are commonly regarded as standard candles, supports the accelerating universe.





The figure above shows that near 90% of the 42 Type Ia supernovae studied exhibit redshift corresponding to a universe that is accelerating. Of course, this discovery re-introduced the cosmological constant Einstein once theorized, though now in the form of dark energy.

Due to the curvature of the Type V model, CMB anisotropies are constrained to a small region in the sky, termed the ``hot spot'' (Bajtlik et al, 1985). By numerically integrating the equations of the null geodesics for various values of \Omega_{0}, they were able to constrain limits on temperature anisotropy. The figures below show the results. Note that recent evidence supports this type of ``hot spot''. A 2007 collaboration of European scientists discovered a localized fluctuation in the temperature of the CMB in the Virgo cluster. The first reaction to this is that it may be a result of a cosmic defect that formed very early in the universe and subsequently affected last scattering of the CMB (Cruz et al, 2007).

3.3 Bianchi Type IX Model

Discuss the metric and general properties

3.3.1 Mixmaster Universe

Add

4 Anisotropic Decay

Viscosity (Misner, 1968a&b) / particle creation (MTW)

5 References

Bajtlik et al. 1985. 

[Maksi]

What detailled error message do you get when you click on “Undefined control sequence”? What document class do you use, which version of LyX and LaTeX and how does your preamble look like? (Copy and paste the code from your LaTeX preamble in Document -> Settings (if there is any code))

[astroryan7]

Here is a screenshot of the error message (attached). I use LyX 1.5.2, and the Document Class is "article". And here is my preamble:

Code: Select all

\jurabibsetup{%titleformat=italic,%titleformat=commasep,%commabeforerest,%ibidem=strict,%citefull=first,%lookat,%oxford,%pages=format,%idem%}

I pasted this in when I was trying to figure out how to format the bibliography (which I'm not concerned with at this point).

Thanks again.

-Ryan

[astroryan7]

FYI, I just took out the preamble, and it worked (converted to PDF). Thanks for the heads up and both of your guys' help.

-Ryan

[Maksi]

Okay, just to explain you a few things:

1. If you get a LaTeX error in LyX, LyX will take you to the place of the error in the document and mark it. If it marks the very beginning of the document as in your example, it means that something within the preamble is not well configured (cf. attachment one).

   

   bild1.jpg (27.66 KiB) Viewed 10457 times

2. What I meant by clicking on Undefined control sequence was that I asked you to click on the line. In the window below you would have gotten a more detailed error message then and only with that one we can help you (cf. attachment two).

   

   bild2.jpg (15.7 KiB) Viewed 10456 times

From your posts above I would say that there was a problem with your Jurabib-configuration. If you need help setting up your references, feel free to ask. Generally, LyX offers three citation modes:

1. citation by numbers as is standard in LaTeX and the (some?) natural sciences -> check Numerical/Default in LyX: Document -> Settings -> Bibliography
2. citation in author-year format as is common in social sciences -> check Natbib in LyX: Document -> Settings -> Bibliography
3. citation with footnotes as is common in humanities -> check Jurabib in LyX: Document -> Settings -> Bibliography